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Hokkaido University Preprint Series in Mathematics >
Global estimates of maximal operators generated by dispersive equations
| 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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Submitter: 数学紀要登録作業用
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