Mathematics (Sep 2022)

<i>A</i><sub><i>p</i></sub> Weights in Directionally (<i>γ</i>,<i>m</i>) Limited Space and Applications

  • Yu Yan,
  • Yiming Wang,
  • Yiming Lei

DOI
https://doi.org/10.3390/math10193454
Journal volume & issue
Vol. 10, no. 19
p. 3454

Abstract

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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 Ap(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.

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