The Generalized Mehler–Fock Transform over Lebesgue Spaces

Abstract

This paper focuses on establishing boundedness properties and Parseval–Goldstein-type relations for the generalized Mehler–Fock transform initially introduced by B. L. J. Braaksma and B. M. Meulenbeld (Compositio Math., 18(3):235–287, 1967). Also, we derive an inversion formula for this transform over Lebesgue spaces.

Keywords

• generalized Mehler–Fock transform
• Lebesgue spaces
• inversion formula
• boundedness properties
• Parseval–Goldstein-type relations