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Global estimates of maximal operators generated by dispersive equations

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 Title: Global estimates of maximal operators generated by dispersive equations Authors: Cho, Yonggeun Browse this author Shim, Yongsun Browse this author Keywords: dispersive equation maximal operator Sobolev space Besov space phase function Issue Date: 2005 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 704 Start Page: 1 End Page: 13 Abstract: Let $Tf(x,t) = e^{2\pi it\phi(D)}f$ 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69509 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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