On <i>L</i>^<i>p</i>-Boundedness Properties and Parseval–Goldstein-Type Theorems for a Lebedev-Type Index Transform

Abstract

This paper investigates Parseval–Goldstein-type relations for a Lebedev-type index transform and examines its behavior in weighted Lebesgue spaces. Key results on Lp-boundedness establish conditions that support these relations. This contributes to understanding the functional framework of Lebedev-type index transforms in mathematical analysis.

Keywords

• Lebedev-type index transform
• modified Bessel (or the Macdonald) function
• weighted Lebesgue spaces
• Parseval–Goldstein relations
• <i>L^p</i>-boundedness properties