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April 16, 2026FilomatOpen Access

Sobolev-type theorem for commutators of variable Marcinkiewicz fractional in grand variable Herz-Morrey spaces

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This research aims to explore the boundedness of commutators of variable Marcinkiewicz fractional operators in grand variable Herz-Morrey spaces.
Defined the variable Marcinkiewicz fractional integral operator using a specific integral formulation.
Utilized the normalized Lebesgue measure on the unit sphere Rn.
Analyzed the boundedness of the commutators on grand variable Herz-Morrey spaces.
Demonstrated that commutators of the Marcinkiewicz fractional operator are bounded on the specified function spaces.
Provided a new perspective on the behavior of these operators in variable spaces.

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Sobolev-type theorem reveals boundedness of commutators in variable Herz-Morrey spaces, indicating a new understanding of integral operators.

Sultan et al. (2025) studied this question.

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Sobolev-type theorem reveals boundedness of commutators in variable Herz-Morrey spaces, indicating a new understanding of integral operators.