Parabolic wavelet transforms and Lebesgue spaces of parabolic potentials

ALİYEV İ., Rubin B.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.32, no.2, pp.391-408, 2002 (SCI-Expanded) identifier identifier

  • 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.