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Criteria of a Two-Weight, Weak-Type Inequality in Orlicz Classes for Maximal Functions Defined on Homogeneous Spaces

Author

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  • Erxin Zhang

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, China)

Abstract

In this study, some new necessary and sufficient conditions for a two-weight, weak-type maximal inequality of the form φ 1 ( λ ) ∫ { x ∈ X : M f ( x ) > λ } ϱ ( x ) d μ ( x ) ≤ c ∫ X φ 2 c | f ( x ) | σ ( x ) d μ ( x ) are obtained in Orlicz classes, where M f is a Hardy–Littlewood maximal function defined on homogeneous spaces and ϱ is a weight function.

Suggested Citation

  • Erxin Zhang, 2024. "Criteria of a Two-Weight, Weak-Type Inequality in Orlicz Classes for Maximal Functions Defined on Homogeneous Spaces," Mathematics, MDPI, vol. 12(14), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2271-:d:1439271
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