报告人：Kato Tomoya (Osaka University, JAPAN)
时间：2018-08-23 16:00-17:00
地点：Room 1365, Sciences Building No. 1
Abstract: In this talk, for $F(f)$, compositions of functions $F$ and $f$, we consider the question whether the following claim holds: ``If $f$ belongs to a function space, then $F(f)$
belongs to the same function space." For the simple example $F(f) = f^2$, if the function space is a multiplication algebra, this claim holds true. For general functions $F$, Bony (1981)
and Meyer (1981) proved that if $F$ is smooth and $F(0)=0$, then the claim mentioned above holds true on the $L^p$-Sobolev space $H^s_p (\mathbb{R}^n)$ with $s > n/p$,
which is embedded into $L^\infty (\mathbb{R}^n)$ and a multiplication algebra. In this talk, we consider whether the claim for the general functions treated by Bony and Meyer holds on
modulation spaces. This is a joint work with Prof. M. Sugimoto (Nagoya) and Prof. N. Tomita (Osaka).
