Weighted HLS inequalities for radial functions and Strichartz estimates for wave and Schroedinger equations
Abstract
This paper is concerned with derivation of the global or local in time Strichartz estimates for radially symmetric solutions of the free wave equation from some Morawetztype estimates via weighted HardyLittlewoodSobolev (HLS) inequalities. In the same way we also derive the weighted endpoint Strichartz estimates with gain of derivatives for radially symmetric solutions of the free Schroedinger equation. The proof of the weighted HLS inequality for radially symmetric functions involves an application of the weighted inequality due to Stein and Weiss and the HardyLittlewood maximal inequality in the weighted Lebesgue space due to Muckenhoupt. Under radial symmetry we get significant gains over the usual HLS inequality and Strichartz estimate.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.1933
 Bibcode:
 2007arXiv0711.1933H
 Keywords:

 Mathematics  Analysis of PDEs;
 35L05;
 35Q55 (Primary);
 35B65 (Secondary)
 EPrint:
 24 pages. To appear in Illinois Journal of Mathematics