BOUNDEDNESS OF GENERALIZED FRACTIONAL INTEGRALS ON GENERALIZED WEIGHTED MORREY SPACES OVER METRIC MEASURE SPACES AND APPLICATIONS

Authors

DOI:

https://doi.org/10.25077/jmua.15.1.1-16.2026

Keywords:

sublinear operator, generalized weighted Morrey space, metric measure space, Dirichlet problem

Abstract

In this paper we investigate the boundedness properties of generalized fractional integral on generalized weighted Morrey spaces over metric measure spaces. The measure used in this paper is a doubling measure which satisfies the growth condition. The results show that the generalized fractional integral is bounded from one generalized weighted Morrey spaces to another generalized weighted Morrey space over metric measure spaces either with the same or with the different parameters. Our results extend the known results for fractional integrals on generalized Morrey spaces. We then investigate the regularity of the solution of Dirichlet problem with the data in generalized weighted Morrey spaces by using the boundedness properties of the generalized fractional integral on generalized weighted Morrey space.

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Published

26-01-2026

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Vol. 15 No. 1 (2026)

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