Hardy-Littlewood, Bessel-Riesz, and Fractional Integral Operators in Anisotropic Morrey and Campanato Spaces

Michael V. Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov

2018

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DOI 10.1515/fca-2018-0032

Data confidence 70 medium

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Abstract

We analyze local (central) Morrey spaces, generalized local (central) Morrey spaces and Campanato spaces on homogeneous groups. The boundedness of the Hardy-Littlewood maximal operator, Bessel-Riesz operators, generalized Bessel-Riesz operators and generalized fractional integral operators in generalized local (central) Morrey spaces on homogeneous groups is shown. Moreover, we prove the boundedness of the modified version of the generalized fractional integral operator and Olsen type inequalities in Campanato spaces and generalized local (central) 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.