A maximal inequality associated to Schr\{o}dinger type equation.
Preprint Series # 685 Cho, Yonggeun and Lee, Sanghyuk and Shim, Yongsun A maximal inequality associated to Schr\{o}dinger type equation. (2005); AbstractIn this note, we consider a maximal operator $\sup_{t \in
\mathbb{R}}u(x,t) = \sup_{t \in \mathbb{R}}e^{it\Omega(D)}f(x)$,
where $u$ is the solution to the initial value problem $u_t =
i\Omega(D)u$, $u(0) = f$ for a $C^2$ function $\Omega$ with some
growth rate at infinity. We prove that the operator $\sup_{t \in
\mathbb{R}}u(x,t)$ has a mapping property from a fractional
Sobolev space $H^\frac14$ with additional angular regularity to
$L_{loc}^2$. Item Type:  Preprint 

Additional Information:  10 copies 

Uncontrolled Keywords:  Schr\"{o}dinger type
equation, maximal operator, angular regularity 

Subjects:  42xx FOURIER ANALYSIS 

ID Code:  844 

