On the Boundedness of Integral Operators in Weighted Grand Morrey Spaces

V. M. Kokilashvili ; A. N. Meskhi

Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 203-215.

Résumé

We obtain boundedness criteria in terms of Muckenhoupt weights for the Hardy–Littlewood maximal operator and Riesz transforms in weighted grand Morrey spaces $M^{p),q,\varphi }_w$. We also consider some structural properties of the spaces $M^{p),q,\varphi }_w$. The spaces are defined, generally speaking, on spaces of homogeneous type. The results are new even in the case of a special function $\varphi $.

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