Bounded operators on mixed norm Lebesgue spaces
Nikita Evseev, Alexander Menovschikov
TL;DR
This paper investigates bounded operators on mixed norm Lebesgue spaces, providing a complete characterization of composition operators, sufficient conditions for integral operators, and applications to Hardy-Steklov operators.
Contribution
It offers the first comprehensive description of bounded composition operators and new boundedness criteria for integral operators on mixed norm Lebesgue spaces.
Findings
Complete characterization of bounded composition operators.
Sufficient conditions for boundedness of certain integral operators.
Application of techniques to Hardy-Steklov type operators.
Abstract
We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain class of integral operators, we provide sufficient conditions for boundedness. We conclude by applying the developed technique to the investigation of Hardy-Steklov type operators.
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