Parabolic wavelet transforms and lebesgue spaces of parabolic potentials

Ilham A. Aliev; Boris Rubin

doi:10.1216/rmjm/1030539677

Parabolic wavelet transforms and lebesgue spaces of parabolic potentials

Ilham A. Aliev
, Boris Rubin

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

Parabolic wavelet transforms associated with heat operators − D_x + ∂/∂t and I − D_x + ∂/∂t in Rⁿ⁺¹ are introduced. A Calder Lon-ype reproducing formula for functions f ∈ L^p(Rⁿ⁺¹) is proven. By making use of these transforms, new explicit inversion formulas for the Jones-Sampson parabolic potentials are obtained, and characterization of the corresponding anisotropic Lebesgue spaces is given.

Original language	English
Pages (from-to)	391-408
Number of pages	18
Journal	Rocky Mountain Journal of Mathematics
Volume	32
Issue number	2
DOIs	https://doi.org/10.1216/rmjm/1030539677
State	Published - 2002

Keywords

Anisotropic Lebesgue spaces
Calderón’s reproducing formula
Parabolic potentials
Wavelet transforms

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KW - Anisotropic Lebesgue spaces

KW - Calderón’s reproducing formula

KW - Parabolic potentials

KW - Wavelet transforms

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Parabolic wavelet transforms and lebesgue spaces of parabolic potentials

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