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Windowed-Kontorovich-Lebedev transforms |
Jiman ZHAO1( ), Lizhong PENG2 |
| 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 |
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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.
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| Keywords
Kontorovich-Lebedev transform
translation
Weyl operator
Windowed-Kontorovich-Lebedev transform
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Corresponding Author(s):
ZHAO Jiman,Email:jzhao@bnu.edu.cn
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Issue Date: 05 December 2010
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