What question did this study set out to answer?

The aim is to analyze the boundedness of rough Hardy operators in variable exponent Morrey–Herz spaces and explore related commutator estimates.

May 20, 2026Open Access

Boundedness Results and Commutator Inequalities for Rough Hardy Operators on Variable Exponent Morrey–Herz Spaces

Key Points

The aim is to analyze the boundedness of rough Hardy operators in variable exponent Morrey–Herz spaces and explore related commutator estimates.
Conducted a rigorous analysis of rough Hardy operators within variable exponent Morrey–Herz spaces.
Established quantitative bounds for associated commutator operators under variable exponent BMO conditions.
Demonstrated that rough Hardy operators exhibit boundedness in variable exponent Morrey–Herz spaces.
Provided precise estimates for commutator operators, affirming their behavior in the context of variable exponent BMO.

Abstract

Within the present scholarly exposition, a meticulous and rigorous analysis is undertaken to investigate the boundedness characteristics of rough Hardy operators in the refined structural setting of variable exponent Morrey–Herz spaces. Moreover, parallel and quantitatively precise estimates are systematically established for the associated commutator operators, under the fundamental premise that the underlying symbol functions reside in the variable exponent bounded mean oscillation space (BMO).

Boundedness Results and Commutator Inequalities for Rough Hardy Operators on Variable Exponent Morrey–Herz Spaces

Key Points

Abstract

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