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A Study of One-Sided Singular Integral and Function Space via Reproducing Formula

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Abstract

In this paper, we systematically establish the theory of one-sided Hardy spaces, including Littlewood–Paley g functions, S-square functions and atomic decomposition. Moreover, we further give the characterizations of one-sided Triebel–Lizorkin spaces and the boundedness for commutators. These results complement the missing components in the one-sided singular integral operator and function space theory studied before.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Linyi University, Linyi, 276005, China

    Zunwei Fu & Xianming Hou

  2. College of Information Technology, The University of Suwon, Hwaseong-si, 18323, South Korea

    Zunwei Fu

  3. Department of Mathematics, National Central University, Chung-Li, 320, Taiwan

    Ming-Yi Lee

  4. Department of Mathematics, Macquarie University, Sydney, NSW, 2109, Australia

    Ji Li

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  1. Zunwei Fu
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  2. Xianming Hou
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  4. Ji Li
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Correspondence to Xianming Hou.

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Supported by the National Natural Foundation of China (Nos. 12071197, 12171221, 12271232) and the Natural Science Foundation of Shandong Province (Nos. ZR2020QA006, ZR2021MA031) and the ARC Discovery Project (Grant No. DP220100285) and MOST of Taiwan (Grant No. 110-2115-M-008-009-MY2).

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Fu, Z., Hou, X., Lee, MY. et al. A Study of One-Sided Singular Integral and Function Space via Reproducing Formula. J Geom Anal 33, 289 (2023). https://doi.org/10.1007/s12220-023-01340-8

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