調和解析駒場セミナー

過去の記録 ~03/28次回の予定今後の予定 03/29~

開催情報 土曜日 13:00~18:00 数理科学研究科棟(駒場) 128号室
担当者 小林政晴(北海道大学), 筒井容平(信州大学), 澤野嘉宏(首都大学東京), 寺澤祐高(名古屋大学), 田中仁(東京大学), 古谷康雄(東海大学), 宮地晶彦(東京女子大学)
備考 このセミナーは,月に1度程度,不定期に開催されます.

2013年01月26日(土)

13:30-18:00   数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
胡 国栄
(東京大学) 13:30-15:00
On Triebel-Lizorkin spaces on Stratified Lie groups
(ENGLISH)
[ 講演概要 ]
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.

小野寺 有紹
(九州大学) 15:30-17:00
Profiles of solutions to an integral system related to
the weighted Hardy-Littlewood-Sobolev inequality
(JAPANESE)
[ 講演概要 ]
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.