## Harmonic Analysis Komaba Seminar

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

### 2013/01/26

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
(ENGLISH)
[ 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
(JAPANESE)
[ 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
infinity.
This work extends previous results obtained by other authors to the
general case.