Global estimates of maximal operators generated by dispersive equations
Preprint Series # 704 Cho, Yonggeun and Shim, Yongsun Global estimates of maximal operators generated by dispersive equations. (2005); AbstractLet $Tf(x,t) = e^{2\pi it\phi(D)}f$ be the solution of of the
general dispersive equation with the phase function $\phi$ and
initial data $f$ in the Schwartz class. In case that the phase
$\phi$ has a suitable growth rate at the infinity and the origin
and $f$ is a finite linear combination of radial and spherical
harmonic functions, we have global $L^p$ estimates of maximal
operator defined by taking the supremum w.r.t. $t$. In particular,
we obtain a global estimate at the end point left open. Item Type:  Preprint 

Additional Information:  10 

Uncontrolled Keywords:  dispersive equation,
maximal operator, Sobolev space, Besov space, phase function 

Subjects:  42xx FOURIER ANALYSIS 

ID Code:  883 

