Acta Mathematica Sinica, English Series

, Volume 26, Issue 11, pp 2071–2084

Boundedness of an oscillating multiplier on Triebel-Lizorkin spaces

Article

DOI: 10.1007/s10114-010-9573-6

Cite this article as:
Cao, W., Chen, J.C. & Fan, D.S. Acta. Math. Sin.-English Ser. (2010) 26: 2071. doi:10.1007/s10114-010-9573-6

Abstract

In this paper, we study Triebel-Lizorkin space estimates for an oscillating multiplier mΩ,α,β. This operator was initially studied by Wainger and by Fefferman-Stein in the Lebesgue spaces. We obtain the boundedness results on the Triebel-Lizorkin space Ḟpα,q (ℝn) for different p, q.

Keywords

Oscillating multiplier Triebel-Lizorkin spaces atomic decomposition 

MR(2000) Subject Classification

42B25 42B15 42B99 

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouP. R. China
  2. 2.Department of MathematicsUniversity of Wisconsin-MilwaukeeMilwaukeeUSA