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September 10, 2025Open Access

Boundedness of some operators in grand generalized weighted Morrey spaces on RD-spaces

Key Points

Boundedness of the Hardy-Littlewood maximal operator is proven for functions in grand generalized weighted Morrey spaces.
The ?-type Calderón-Zygmund operator is shown to be bounded under specific conditions in these weighted spaces.
The results regarding the commutator generated by the Calderón-Zygmund operator expand knowledge in both weighted Morrey and Euclidean domains.
New findings illustrate the applicability of such operators in complex RD-spaces, enhancing functional analysis.

Abstract

This paper aims to investigate the boundedness of some operators on grand generalized weighted Morrey spaces Lp),??(?) over RD-spaces. Under assumption that functions ? and ? satisfy certain conditions, we prove that Hardy-Littlewood maximal operator and ?-type Calder?n-Zygmund operator are bounded on these spaces. Moreover, the boundedness of the commutator b,T? generated by the ?-type Calderon-Zygmund operator and locally integrable function b is also established. The results presented for grand generalized weighted Morrey spaces are also new even in the context of Euclidean domains.

Boundedness of some operators in grand generalized weighted Morrey spaces on RD-spaces

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Abstract

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