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November 2008 Global estimates of maximal operators generated by dispersive equations
Yonggeun CHO, Yongsun SHIM
Hokkaido Math. J. 37(4): 773-794 (November 2008). DOI: 10.14492/hokmj/1249046368


Let $Tf(x, t) = e^{itφ(D)f}$ be the solution of a general dispersive equation with phase function φ and initial data $f$ in a Sobolev space. When the phase φ has a suitable growth condition and the initial data f has an angular regularity, we prove global and local L^p estimates for maximal operators generated by T. Here we do not assume the radial symmetry for the initial data. These results reveal some sufficient conditions on initial data for the boundedness of maximal operators in contrast to the negative results of [28]. We also prove a weighted L^2 maximal estimate, which is an extension of [19] to nonradial initial data.


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Yonggeun CHO. Yongsun SHIM. "Global estimates of maximal operators generated by dispersive equations." Hokkaido Math. J. 37 (4) 773 - 794, November 2008.


Published: November 2008
First available in Project Euclid: 31 July 2009

zbMATH: 1171.42006
MathSciNet: MR2474175
Digital Object Identifier: 10.14492/hokmj/1249046368

Primary: 42B25
Secondary: 42A45

Rights: Copyright © 2008 Hokkaido University, Department of Mathematics


Vol.37 • No. 4 • November 2008
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