RESEARCH ARTICLE

Windowed-Kontorovich-Lebedev transforms

  • Jiman ZHAO , 1 ,
  • Lizhong PENG 2
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  • 1. School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing 100875, China
  • 2. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

Received date: 08 Dec 2009

Accepted date: 05 Jun 2010

Published date: 05 Dec 2010

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

The aim of this paper is to study the boundedness of the windowed-Kontorovich-Lebedev transforms. For this purpose, we first define the translation associated to the Kontorovich-Lebedev transform and a generalized convolution product, then obtain some harmonic analysis results. We present a sufficient and necessary condition for the boundedness of the windowed-Kontorovich-Lebedev transform. Finally, we define the corresponding Weyl operator, and study the boundedness and compactedness of the Weyl operator with symbols in Lq (q ∈ [1, 2]) acting on Lp.

Cite this article

Jiman ZHAO , Lizhong PENG . Windowed-Kontorovich-Lebedev transforms[J]. Frontiers of Mathematics in China, 2010 , 5(4) : 777 -792 . DOI: 10.1007/s11464-010-0082-9

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