Open Access Research

Hypersingular integral operators on modulation spaces for 0 < p < 1

Meifang Cheng

Author Affiliations

School of Mathematical and Computer Sciences, Anhui Normal University, Wuhu, 241003, People’s Republic of China

Journal of Inequalities and Applications 2012, 2012:165 doi:10.1186/1029-242X-2012-165

Published: 23 July 2012

Abstract

The purpose of this paper is to investigate the mapping properties of the hypersingular integral operators on general weighted modulation spaces <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/165/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/165/mathml/M2">View MathML</a> for <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/165/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/165/mathml/M1">View MathML</a>. Our results show that modulation spaces are good substitutions for Lebesgue spaces.

MSC: 42B20, 42B25.

Keywords:
hypersingular integral operator; modulation space; Fourier multiplier