Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces

TL;DR

This paper investigates the boundedness of various integral operators in Morrey and Campanato spaces on homogeneous groups, extending classical Euclidean results to more general anisotropic settings.

Contribution

It establishes boundedness results for Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in generalized Morrey and Campanato spaces on homogeneous groups, including some novel Euclidean cases.

Findings

Boundedness of Hardy-Littlewood maximal operator in generalized Morrey spaces.

Boundedness of Bessel-Riesz and fractional integral operators in these spaces.

Extension of classical Euclidean results to anisotropic homogeneous groups.

Abstract

We analyse Morrey spaces, generalised Morrey spaces and Campanato spaces on homogeneous groups. The boundedness of the Hardy-Littlewood maximal operator, Bessel-Riesz operators, generalised Bessel-Riesz operators and generalised fractional integral operators in generalised Morrey spaces on homogeneous groups is shown. Moreover, we prove the boundedness of the modified version of the generalised fractional integral operator and Olsen type inequalities in Campanato spaces and generalised Morrey spaces on homogeneous groups, respectively. Our results extend results known in the isotropic Euclidean settings, however, some of them are new already in the standard Euclidean cases.