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A p Weights in Directionally ( γ , m ) Limited Space and Applications

Author

Listed:
  • Yu Yan

    (School of Economics, Peking University, Beijing 100871, China
    These authors contributed equally to this work.)

  • Yiming Wang

    (School of Economics, Peking University, Beijing 100871, China
    Key Laboratory of Mathematical Economics and Quantitative Finance, Beijing 100871, China
    These authors contributed equally to this work.)

  • Yiming Lei

    (PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100034, China
    These authors contributed equally to this work.)

Abstract

Let ( X , d ) be a directionally ( γ , m ) -limited space with every γ ∈ ( 0 , ∞ ) . In this setting, we aim to study an analogue of the classical theory of A p ( μ ) weights. As an application, we establish some weighted estimates for the Hardy–Littlewood maximal operator. Then, we introduce the relationship between directionally ( γ , m ) -limited spaceand geometric doubling. Finally, we obtain the weighted norm inequalities of the Calderón–Zygmund operator and commutator in non-homogeneous space.

Suggested Citation

  • Yu Yan & Yiming Wang & Yiming Lei, 2022. "A p Weights in Directionally ( γ , m ) Limited Space and Applications," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3454-:d:922215
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    References listed on IDEAS

    as
    1. Feng Liu & Seongtae Jhang & Sung-Kwun Oh & Zunwei Fu, 2019. "Variation Inequalities for One-Sided Singular Integrals and Related Commutators," Mathematics, MDPI, vol. 7(10), pages 1-19, September.
    2. Yongliang Zhou & Dunyan Yan & Mingquan Wei, 2020. "Boundedness of a Class of Oscillatory Singular Integral Operators and Their Commutators with Rough Kernel on Weighted Central Morrey Spaces," Mathematics, MDPI, vol. 8(9), pages 1-16, August.
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