Bilinear integral operator on Morrey-Banach spaces and its application

TL;DR

This paper investigates the boundedness and definability of bilinear integral operators and their commutators on Morrey-Banach spaces, establishing conditions related to BMO and extending results to weighted and variable exponent Morrey spaces.

Contribution

It introduces new boundedness results for bilinear integral operators and commutators on Morrey-Banach spaces, including necessary conditions for BMO and applications to variable exponent spaces.

Findings

Boundedness of bilinear singular and fractional integral operators on Morrey-Banach spaces.

Necessary conditions for BMO via boundedness of bilinear commutators.

Boundedness of bilinear Calderón-Zygmund operators on Morrey spaces with variable exponents.

Abstract

In this paper, we give the definability of bilinear singular and fractional integral operators on Morrey-Banach space, as well as their commutators and we prove the boundedness of such operators on Morrey-Banach spaces. Moreover, the necessary condition for BMO via the bounedness of bilinear commutators on Morrey-Banach space is also given. As a application of our main results, we get the necessary conditions for BMO via the bounedness of bilinear integral operators on weighted Morrey space and Morrey space with variable exponents. Finally, we obtain the boundedness of bilinear C-Z operator on Morrey space with variable exponents.