The inclusion relation between Sobolev and modulation spaces

Masaharu Kobayashi, Mitsuru Sugimoto

Published 2010-09-05, updated 2010-09-07Version 2

The inclusion relations between the $L^p$-Sobolev spaces and the modulation spaces is determined explicitly. As an application, mapping properties of unimodular Fourier multiplier $e^{i|D|^\alpha}$ between $L^p$-Sobolev spaces and modulation spaces are discussed.