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Limiting Weak-Type Behaviors for Certain Classical Operators in Harmonic Analysis

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Abstract

This paper explores the limiting weak-type behaviors of certain classical operators in harmonic analysis including maximal operators, singular and fractional integral operators and maximal truncated singular integrals as well as the general convolution operators with weak-type Young’s inequalities. Some optimal limiting weak-type behaviors are given, which essentially improve and extend the previous results. As applications, several characterizations on the weak-type endpoint boundedness for fractional integral operators and maximal operators with homogeneous kernels, and the weak-type Young’s inequality for the general convolution operator are also obtained.

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Acknowledgments

Supported by the NNSF of China (Nos.11771358, 11871101, 11701112, 11671414) and the China Postdoctoral Science Foundation (No. 2017M612628).

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Authors and Affiliations

  1. School of Science, Jimei University, Xiamen, 361021, China

    Weichao Guo

  2. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China

    Jianxun He

  3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Huoxiong Wu

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  1. Weichao Guo
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  2. Jianxun He
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  3. Huoxiong Wu
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Correspondence to Huoxiong Wu.

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Guo, W., He, J. & Wu, H. Limiting Weak-Type Behaviors for Certain Classical Operators in Harmonic Analysis. Potential Anal 54, 307–330 (2021). https://doi.org/10.1007/s11118-020-09828-6

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  • DOI: https://doi.org/10.1007/s11118-020-09828-6

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