Inhomogeneous oscillatory integrals and global smoothing effects for dispersive equations
Abstract
We study oscillatory integrals of the type F-1 (e ita (ṡ) ψ (ṡ)) where a is a general function satisfying some elliptic type and non-degenerate conditions at both the origin and the infinity, and ψ belongs to some symbol class. Point-wise estimates in space-time are gained with partial sharpness. As applications, global smoothing effects of Lp-Lq as well as Strichartz type for dispersive equations are studied. An application to fractional Schrödinger equations is also given.
- Publication:
-
Journal of Differential Equations
- Pub Date:
- December 2017
- DOI:
- 10.1016/j.jde.2017.08.053
- arXiv:
- arXiv:1612.09072
- Bibcode:
- 2017JDE...263.8606H
- Keywords:
-
- Oscillatory integrals;
- Dispersive equations;
- L<SUP>p</SUP>-L<SUP>q</SUP> estimates;
- Mathematics - Analysis of PDEs;
- Mathematics - Classical Analysis and ODEs
- E-Print:
- 22 pages, 1 figure