Parabolic wavelet transforms and Lebesgue spaces of parabolic potentials
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.32, no.2, pp.391-408, 2002 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 32 Issue: 2
- Publication Date: 2002
- Doi Number: 10.1216/rmjm/1030539677
- Journal Name: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.391-408
- Keywords: wavelet transforms, parabolic potentials, Calderon's reproducing formula, anisotropic Lebesgue spaces
- Akdeniz University Affiliated: Yes
Abstract
Parabolic wavelet transforms associated with heat operators -D-x + partial derivative/partial derivativet and I - D-x + partial derivative/partial derivativet in Rn+1 are introduced. A Calderon-type reproducing formula for functions f is an element of 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.