## Harmonic Analysis Komaba Seminar

Seminar information archive ～06/03｜Next seminar｜Future seminars 06/04～

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

### 2016/01/09

**Hitoshi Tanaka**(Tokyo University) 13:30-15:00

The n linear embedding theorem

(日本語)

**Kentaro Hirata**(Hiroshima University) 15:30-17:00

An improved growth estimate for positive solutions of a semilinear heat equation in a Lipschitz domain

(日本語)

### 2015/11/14

### 2015/10/03

**Tomoya Kato**(Nagoya University) 13:30-15:00

Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces

(日本語)

**Naohito Tomita**(Osaka University) 15:30-17:00

On multilinear Fourier multipliers with minimal Sobolev regularity

(日本語)

### 2015/07/11

**Mitsuo Izuki**(Okayama University) 13:30 -15:00

An intrinsic square function on weighted Herz spaces with variable exponent

(日本語)

**Toshio Horiuchi**(Ibaraki University) 15:30 -17:00

Remarks on the strong maximum principle involving p-Laplacian

(日本語)

### 2015/05/02

**Hitoshi Tanaka**(Univ Tokyo) 13:30-15:00

Two-weight Morrey norm inequality and the sequential testing

(日本語)

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 ${\mathcal S}_0$

(日本語)

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

and

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.

### 2015/01/10

**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)

### 2014/11/22

**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)

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)

T.B.A.

**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)

T.B.A.

### 2014/10/25

**Yoshihiro Sawano**(Tokyo Metropolitan University) 13:30-14:30

Approximation in Banach space by linear positive operators (JAPANESE)

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)

### 2014/06/28

**Neal Bez**(埼玉大学) 13:30-15:00

On the multilinear restriction problem (ENGLISH)

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)

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.

### 2014/05/17

**Yohei Tsutsui**(The University of Tokyo) 13:30-15:00

Bounded small solutions to a chemotaxis system with non-diffusive chemical (JAPANESE)

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)

### 2014/04/19

**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)

### 2014/02/15

**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)

### 2014/01/25

**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)

### 2013/11/16

**Guorong Hu**(The University of Tokyo) 13:30-15:00

Besov and Triebel-Lizorkin spaces associated with

non-negative self-adjoint operators

(ENGLISH)

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

$P_{t}=e^{-tL}$

generated by $L$ consists of integral operators with (heat) kernel

$p_{t}(x,y)$

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)

### 2013/10/12

**Tomoya Kato**(Nagoya University) 13:30-15:00

The global Cauchy problems for nonlinear dispersive equations on modulation spaces

(JAPANESE)

**Naoto Kumanogo**(Kogakuin University) 15:30-17:00

Path Integrals--Analysis on path space by time-slicing method (JAPANESE)

### 2013/07/20

**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

(JAPANESE)

**Naohito Tomita**(Osaka University) 15:30-17:00

On the smoothness conditions for bilinear Fourier multipliers (JAPANESE)

### 2013/06/29

**Yoshihiro Sawano**(Tokyo Metropolitan University) 13:30-15:00

Critical Sobolev embedding of function spaces and the real interpolation functor

(JAPANESE)

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

(JAPANESE)

### 2013/05/25

**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

(JAPANESE)

### 2013/04/20

**Hiroki Saito**(Tokyo Metropolitan University) 13:30-15:00

Directional maximal operators and radial weights on the plane

(JAPANESE)

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

exponents

(JAPANESE)

### 2013/01/26

**Guorong, Hu**

(Tokyo Univesity) 13:30-15:00

On Triebel-Lizorkin spaces on Stratified Lie groups

(ENGLISH)

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

(JAPANESE)

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

infinity.

This work extends previous results obtained by other authors to the

general case.

### 2012/11/10

**Tokio Matsuyama**(Chuo University) 13:00-14:20

Perturbed Besov spaces by short-range type potential

in exterior domains (JAPANESE)

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)

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)

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).

References:

[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.

### 2012/10/06

**Shuichi Sato**(Kanazawa university) 13:30-15:00

Method of rotations with weight for nonisotropic dilations (JAPANESE)

**( ) 15:30-17:00**

TBA (JAPANESE)

### 2012/07/14

**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

(JAPANESE)

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.

### 2012/06/09

**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

(JAPANESE)

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.

### 2012/05/26

**Kiko Kawamura**(University of North Texas) 13:30-15:00

The Takagi function - a survey (JAPANESE)

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)

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).