Exchange Formulae for the Stieltjes–Poisson Transform over Weighted Lebesgue Spaces

Abstract

This paper aims to develop exchange formulae for the Stieltjes–Poisson transform by using Mellin-type convolutions in the context of weighted Lebesgue spaces. A key result is the introduction of bilinear and continuous Mellin-type convolutions, expanding the scope of the analysis to include the space of weighted L1 functions and the space of continuous functions vanishing at infinity.

Keywords

• Stieltjes–Poisson transform
• weighted Lebesgue spaces
• Mellin-type convolutions
• exchange formulae
• continuous functions vanishing at infinity