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Lipschitz estimates for commutator of fractional integral operators on non-homogeneous metric measure spaces

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Abstract

In this paper, the authors establish the (Lp(μ), Lq(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions (b ∈ Lipβ (μ)), where 1 <p < 1/(α + β) and 1/q = 1/p– (α + β), and obtain their weak (L1(μ), L1/(1–α–β) (μ))-type. Moreover, the authors also consider the boundedness in the case that 1 /(α+β) < p < 1/α, 1/α ≤ p ≤ ∞ and the endpoint cases, namely, p = 1/(α + β).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241000, China

    Ding-huai Wang

  2. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

    Jiang Zhou

  3. College of Science and Information Engineering, Jiaxing University, Jiaxing, 314001, China

    Bo-lin Ma

Authors
  1. Ding-huai Wang
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  2. Jiang Zhou
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  3. Bo-lin Ma
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Corresponding author

Correspondence to Ding-huai Wang.

Additional information

Supported by the National Natural Science Foundation of China (Grant No.11661075).

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Wang, Dh., Zhou, J. & Ma, Bl. Lipschitz estimates for commutator of fractional integral operators on non-homogeneous metric measure spaces. Appl. Math. J. Chin. Univ. 35, 253–264 (2020). https://doi.org/10.1007/s11766-020-3319-8

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  • DOI: https://doi.org/10.1007/s11766-020-3319-8

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