Windowed-Kontorovich-Lebedev transforms

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 L^q (q ∈ [1, 2]) acting on L^p.

Keywords

Kontorovich-Lebedev transform / translation / Weyl operator / Windowed-Kontorovich-Lebedev transform

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