On compactness of Laplace and Stieltjes type transformations in Lebesgue spaces

TL;DR

This paper establishes criteria for when Laplace and Stieltjes type integral transformations are compact operators on Lebesgue spaces, enhancing understanding of their functional properties in analysis.

Contribution

It provides new necessary and sufficient conditions for the compactness of these integral transformations on Lebesgue spaces.

Findings

Criteria for compactness of Laplace transformations

Criteria for compactness of Stieltjes transformations

Enhanced understanding of operator properties in Lebesgue spaces

Abstract

We obtain criteria for integral transformations of Laplace and Stieltjes type to be compact on Lebesgue spaces of real functions on the semiaxis.