On the Boundedness of Integral Operators in Weighted Grand Morrey Spaces

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 $.