Harmonic Analysis Komaba Seminar

Seminar information archive ~06/03Next seminarFuture seminars 06/04~

Date, time & place Saturday 13:00 - 18:00 128Room #128 (Graduate School of Math. Sci. Bldg.)

Seminar information archive


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hitoshi Tanaka (Tokyo University) 13:30-15:00
The n linear embedding theorem
Kentaro Hirata (Hiroshima University) 15:30-17:00
An improved growth estimate for positive solutions of a semilinear heat equation in a Lipschitz domain


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Tomoya Kato (Nagoya University) 13:30-15:00
Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces
Naohito Tomita (Osaka University) 15:30-17:00
On multilinear Fourier multipliers with minimal Sobolev regularity


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Mitsuo Izuki (Okayama University) 13:30 -15:00
An intrinsic square function on weighted Herz spaces with variable exponent
Toshio Horiuchi (Ibaraki University) 15:30 -17:00
Remarks on the strong maximum principle involving p-Laplacian


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hitoshi Tanaka (Univ Tokyo) 13:30-15:00
Two-weight Morrey norm inequality and the sequential testing
[ Abstract ]
In this talk we extend Sawyer's two-weight theory to Morrey spaces and give a characterization of two-weight Morrey norm inequalities for the (general) Hardy-Littlewood maximal operators in terms of the sequential testing due to H\"{a}nninen, Hyt\"{o}nen and Li.
We also introduce the description of the K\"othe dual of Morrey type spaces generated by a basis of measurable functions.
The second topic is based on a joint work with Professors Sawano (Tokyo Metropolitan University) and Masty{\l}o (Adam Mickiewicz University and Institute of Mathematics).
Yoshihiro Sawano (Tokyo Metropolitan University.) 15:30-17:00
The topology of the dual space of ${\mathcal S}_0$
[ Abstract ]
Based on the notation of my Japanese book, I will consider the topology of ${\mathcal S}_0'$, the dual of ${\mathcal S}_0$.
In view of the linear isomorphism ${\mathcal S}_0' \sim {\mathcal S}/{\mathcal P}$, we can consider two different topologies;

1) the weak-* topology
2) the quotient topology in ${\mathcal S}/{\mathcal P}$.

We aim to show that these two topologies are the same. This will be an errortum of my Japanese book.
This work is done jointly with Takahiro Noi and Shohei Nakamura in Tokyo Metropolitan University.


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Koichi Kaizuka (Gakushuin University) 13:30-15:00
Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application (JAPANESE)
Norisuke Ioku (Ehime University) 15:30-17:00
スケール不変性を持つ臨界Hardyの不等式について (JAPANESE)


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Denny Hakim (Tokyo Metropolitan University) 13:30-14:30
On the Inclusion of Generalized Morrey Spaces and the Boundedness of the Generalized Fractional Maximal Operators (ENGLISH)
[ Abstract ]
In this talk, we shall prove a necessary and sufficient condition for an inclusion property of generalized Morrey spaces. We use this property in our proof of the boundedness of the generalized fractional maximal operators on these spaces. Our result also cover the generalized weak Morrey spaces.
This research is a joint work with Y. Sawano, H. Gunawan, K.M. Limanta and A.A. Masta.
Tamara Tararykova (Cardiff University / Eurasian National University) 14:45-15:45
Hardy-type inequality for 0 < p < 1 and hypodecreasing functions (ENGLISH)
[ Abstract ]
Victor Burenkov (Cardift School of Mathematics / Peoples' Friendship University of Russia / Steklov Institute of Mathematics) 16:00-17:00
Sharp spectral stability estimate for uniformly elliptic differential operators (EMGLISH)
[ Abstract ]


13:30-16:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiro Sawano (Tokyo Metropolitan University) 13:30-14:30
Approximation in Banach space by linear positive operators (JAPANESE)
[ Abstract ]
We obtain a sufficient condition for the
convergence of positive linear operators in Banach
function spaces on Rn and derive a Korovkin type
theorem for these spaces. Also, we generalized
this result via statistical sense. This is a joint
work with Professor Arash Ghorbanalizadeh.
Tsuyoshi Yoneda (Tokyo Institute of Technology) 15:00-16:30
Local ill-posedness of the Euler equations in a critical Besov space (JAPANESE)


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Neal Bez (埼玉大学) 13:30-15:00
On the multilinear restriction problem (ENGLISH)
[ Abstract ]
I will discuss the multilinear restriction problem for the Fourier transform. This will include an overview of the pioneering work of Bennett, Carbery and Tao on this problem and the very losely connected multilinear Kakeya problem. I will also discuss some of my own work in this area which is connected to nonlinear Brascamp-Lieb inequalities (joint work with Jonathan Bennett).
Hong Yue (Georgia College and State University) 15:30-17:00
John-Nirenberg lemmas for a doubling measure (ENGLISH)
[ Abstract ]
We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yohei Tsutsui (The University of Tokyo) 13:30-15:00
Bounded small solutions to a chemotaxis system with non-diffusive chemical (JAPANESE)
[ Abstract ]
We consider a chemotaxis system with a logarithmic sensitivity and a non-diffusive chemical substance. For some chemotactic sensitivity constants, Ahn and Kang proved the existence of bounded global solutions to the system. An entropy functional was used in their argument to control the cell density by the density of the chemical substance. Our purpose is to show the existence of bounded global solutions for all the chemotactic sensitivity constants. Assuming the smallness on the initial data in some sense, we can get uniform estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu Univ.) and Juan J.L. Vel\\'azquez (Univ. of Bonn).
Toshinao Kagawa (Tokyo City University) 15:30-17:00
Heat kernel and Schroedinger kernel on the Heisenberg group (JAPANESE)


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Ryo Takada (Tohoku University) 13:30-15:00
Strichartz estimates for incompressible rotating fluids (JAPANESE)
Masami Okada (Tokyo Metropolitan Unversity) 15:30-16:30
On the interpolation of functions for scattered data on random infinite points with a sharp error estimate (JAPANESE)


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Batbold Tserendorj (National University of Mongolia) 13:30-15:00
Some Hilbert-type inequalities involving the Hardy operator (ENGLISH)
Masato Kikuchi (University of Toyama) 15:30-17:00
Uniform boundedness of conditinal expectation operators (JAPANESE)


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Jayson Cunanan (Nagoya University) 13:30-15:00
Unimodular Fourier multipliers on Wiener Amalgam Spaces (JAPANESE)
Satoshi Masaki (Hiroshima University) 15:30-17:00
Analysis of mass-subcritical nonlinear Schrödinger equation (JAPANESE)


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Guorong Hu (The University of Tokyo) 13:30-15:00
Besov and Triebel-Lizorkin spaces associated with
non-negative self-adjoint operators
[ Abstract ]
Let $(X,d)$ be a locally compact metric space
endowed with a doubling measure $¥mu$, and
let $L$ be a non-negative self-adjoint operator on $L^{2}(X,d¥mu)$.
Assume that the semigroup
generated by $L$ consists of integral operators with (heat) kernel
enjoying Gaussian upper bound but having no information on the
regularity in the variables $x$ and $y$.
In this talk, we shall introduce Besov and Triebel-Lizorkin spaces associated
with $L$, and
present an atomic decomposition of these function spaces.
Hironobu Sasaki (Chiba University) 15:30-17:00
On asymptotic behavior of solutions for one-dimensional nonlinear Dirac equation (JAPANESE)


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Tomoya Kato (Nagoya University) 13:30-15:00
The global Cauchy problems for nonlinear dispersive equations on modulation spaces
Naoto Kumanogo (Kogakuin University) 15:30-17:00
Path Integrals--Analysis on path space by time-slicing method (JAPANESE)


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yutaka Terasawa (The University of Tokyo) 13:30-15:00
Existence of Weak Solutions for a Diffuse Interface Model of Non-Newtonian Two-Phase Flows
Naohito Tomita (Osaka University) 15:30-17:00
On the smoothness conditions for bilinear Fourier multipliers (JAPANESE)


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiro Sawano (Tokyo Metropolitan University) 13:30-15:00
Critical Sobolev embedding of function spaces and the real interpolation functor
[ Abstract ]
We consider the endpoint case of the Sobolev embedding.
It is well known that the function spaces such as Sobolev spaces are not embedded into L^¥infty in the critical case.
One of the remedies is the Brezis-Gallouet-Wainger type
estimate. However, such an estimate involve the log term
and it can not be regarded as the norm.
In this talk, by using the real interpolation functor, we propose another formulation. We compare
the existing result with our new results.
If time permits, we mention some related results.
Mai Fujita (Osaka University) 15:30-17:00
On weighted estimates for multilinear Fourier multipliers with Sobolev regularity


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Takeshi Iida (Fukushima National College of Technology) 13:30-15:00
Multilinear fractional integral operators on weighted Morrey spaces (JAPANESE)
Yasunori Maekawa (Tohoku University) 15:30-17:00
On factorization of divergence form elliptic operators
and its application


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroki Saito (Tokyo Metropolitan University) 13:30-15:00
Directional maximal operators and radial weights on the plane
[ Abstract ]
Let $\\Omega$ be a set of unit vectors and $w$ be a radial weight on the plane. We consider the weighted directional maximal operator defined by
$M_{\\Omega,w}f(x):=\\sup_{x\\in R\\in \\cB_{\\Omega}}\\frac{1}{w(R)}\\int_{R}|f(y)|w(y)dy$,
where $\\cB_{\\Omega}$ denotes the all rectangles on the plane whose longest side is parallel to some unit vector in $\\Omega$ and $w(R)$ denotes $\\int_{R}w$.
In this talk we give a sufficient condition of the weight
for an almost-orthogonality principle related to these maximal operators to hold. The condition allows us to get weighted norm inequality
$\\|M_{\\Omega,w}f\\|_{L^2(w)}\\le C \\log N \\|f\\|_{L^2(w)}$,
when $w(x)=|x|^a$, $a>0$, and $\\Omega$ is a set of unit vectors on the plane with cardinality $N\\gg 1$.
Takahiro Noi (Chuo University) 15:30-17:00
Boundedness of Trace operator for Besov spaces with variable


13:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Guorong, Hu
(Tokyo Univesity) 13:30-15:00
On Triebel-Lizorkin spaces on Stratified Lie groups
[ Abstract ]
We introduce the notion of Triebel-Lizorkin spaces
$\\dot{F}^{s}_{p,q}(G)$ on a stratified Lie group $G$
in terms of a Littlewood-Paley-type decomposition
with respect to a sub-Laplacian $\\mathscr{L}$ of $G$,
for $s \\in \\mathbb{R}$, $0

We show that the scale of these spaces is actually independent of
the precise choice of the sub-Laplacian
and the Littlewood-Paley-type decomposition.
As we shall see, many properties of the classical
Triebel-Lizorkin spaces on $\\mathbb{R}^{n}$, e.g.,
lifting property, embeddings and dual property,
can be extended to the setting of stratified Lie groups
without too much effort.
We then study the boundedness of convolution operators
on these spaces and finally,
we obtain a Hormander type spectral multipliers theorem.

Michiaki, Onodera (Kyushu University) 15:30-17:00
Profiles of solutions to an integral system related to
the weighted Hardy-Littlewood-Sobolev inequality
[ Abstract ]
We study the Euler-Lagrange system for a variational problem
associated with the weighted Hardy-Littlewood-Sobolev inequality of
Stein and Weiss.
We show that all the nonnegative solutions to the system are radially
symmetric and have particular profiles around the origin and the
This work extends previous results obtained by other authors to the
general case.


13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Tokio Matsuyama (Chuo University) 13:00-14:20
Perturbed Besov spaces by short-range type potential
in exterior domains (JAPANESE)
[ Abstract ]
In this talk we will define perturbed Besov spaces by a short-range potential over exterior domains. These spaces will be available for obtaining the Strichartz estimates of wave equation with a potential in exterior domains.
We will pay attention to observe the equivalence relation between the perturbed Besov spaces and the free ones.
Sugimoto Mitsuru (Nagoya University) 14:40-16:00
Optimal constants and extremisers for some smoothing estimates (JAPANESE)
[ Abstract ]
Our purpose is to study the optimal constant and extremising initial data for a broad class of smoothing estimates for solutions of linear dispersive equations.
Firstly, we discuss the existence/nonexistence of extremisers and then we provide an explicit formula and new observations for the optimal constant.
The talk is based on joint work with Neal Bez (University of Birmingham).
Victor I. Burenkov (Russia/United Kingdom) 16:30-17:50
Spectral stability of the p-Laplacian (JAPANESE)
[ Abstract ]
Dependence of the eigenvalues of the p-Laplacian upon domain perturbation will be under discussion. Namely Lipschitz-type estimates for deviation of the eigenvalues following a domain perturbation will be presented. Such estimates are obtained for the class of open sets admitting open sets with arbitrarily strong degeneration and are expressed in terms of suitable measures of vicinity of two open sets, such as the \\lq\\lq atlas distance" between these sets or the \\lq\\lq lower Hausdor-Pompeiu
deviation" of their boundaries. In the case of open sets with Holder continuous boundaries, our results essentially improve a result known for the rst eigenvalue [2].
Joint work with P. D. Lamberti. The results were recently published in [1].
Supported by the grant of RFBR (project 08-01-00443).

[1] V.I. Burenkov, P.D. Lamberti, Spectral stability of the p-Laplacian, Nonlinear Analysis, 71, 2009, 2227-2235.
[2] J. Fleckinger, E.M. Harrell and F. de Thelin, Boundary behaviour and estimates for solutions for equations containing the p-Laplacian, Electronic Journal of Dierential Equations, 38, 1999, 1-19.


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Shuichi Sato (Kanazawa university) 13:30-15:00
Method of rotations with weight for nonisotropic dilations (JAPANESE)
( ) 15:30-17:00


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hidemitsu Wadade (Gifu University) 13:30-15:00
On various inequalities characterizing critical Sobolev-Lorentz spaces (JAPANESE)
Yoshihiro Sawano (Tokyo Metropolitan University) 15:30-17:00
Boundedness of operators on Hardy spaces with variable exponents
[ Abstract ]
In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:
First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.
Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.
After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yasuo Furuya (Tokai University) 13:30-15:00
Resent topics on the Cauchy integrals (the works of Muscalu and others) (JAPANESE)
Tsukasa Iwabuchi (Chuo University) 15:30-17:00
Ill-posedness for the nonlinear Schr\\"odinger equations in one
space dimension
[ Abstract ]
In this talk, we consider the Cauchy problems for the nonlinear Schr\\"odinger equations. In particular, we study the ill-posedness by showing that the continuous dependence on initial data does not hold. In the known results, Bejenaru-Tao (2006) considered the problem in the Sobolev spaces $H^s (\\mathbb R)$ and showed the ill-posedness when $s < -1 $. In this talk, we study the ill-posedness in the Besov space for one space dimension and in the Sobolev spaces for two space dimensions.


13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Kiko Kawamura (University of North Texas) 13:30-15:00
The Takagi function - a survey (JAPANESE)
[ Abstract ]
More than a century has passed since Takagi published his simple example of a continuous but nowhere differentiable function,
yet Takagi's function -- as it is now commonly referred
to despite repeated rediscovery
by mathematicians in the West -- continues to inspire, fascinate and puzzle researchers as never before.
In this talk, I will give not only an overview of the history and known characteristics of the function,
but also discuss some of the fascinating applications it has found -- some quite recently! -- in such diverse areas of mathematics as number theory, combinatorics, and analysis.
Yutaka Terasawa (The University of Tokyo) 15:30-17:00
Dyadic, classical and martingale harmonic analysis II (JAPANESE)
[ Abstract ]
In a filtered measure space, we investigate the characterization of weights for which positive operators and maximal operators are bounded.

For this, a refinement of Carleson embedding theorem is introduced in this setting. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doob's maximal operator holds is established by an application of our Carleson embedding theorem. If time permits, we would like to mention Hyt\\"onen-P\\'erez type sharp one-weight estimate of Doob's
maximal operator which is derived from our two-weight characterization.
This talk is based on a joint work with Professor Hitoshi Tanaka
(The University of Tokyo).

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