Research article

Weak Hardy spaces associated with para-accretive functions and their applications

  • Received: 07 August 2024 Revised: 11 October 2024 Accepted: 16 October 2024 Published: 28 October 2024
  • MSC : 42B20, 42B25, 42B35

  • In this paper, we introduced a new class of weak Hardy spaces, denoted by $ H^{p, \infty}_b $, and provided an analysis of their atomic decomposition. As an application, we established the boundedness of Calderón-Zygmund operators (CZOs) from $ H^p $ to $ H^{p, \infty}_b $ including cases at the critical exponent

    $ p = \frac{n}{n+\delta}, $

    where $ \delta $ represents the regularity index of the distributional kernel. Moreover, the boundedness of CZOs from $ H^{p, \infty} $ to $ H^{p, \infty}_b $ was demonstrated for

    $ \frac{n}{n+\delta}<p\leq 1. $

    Citation: Yan Wang, Xintian Dong, Fanghui Liao. Weak Hardy spaces associated with para-accretive functions and their applications[J]. AIMS Mathematics, 2024, 9(11): 30572-30596. doi: 10.3934/math.20241476

    Related Papers:

  • In this paper, we introduced a new class of weak Hardy spaces, denoted by $ H^{p, \infty}_b $, and provided an analysis of their atomic decomposition. As an application, we established the boundedness of Calderón-Zygmund operators (CZOs) from $ H^p $ to $ H^{p, \infty}_b $ including cases at the critical exponent

    $ p = \frac{n}{n+\delta}, $

    where $ \delta $ represents the regularity index of the distributional kernel. Moreover, the boundedness of CZOs from $ H^{p, \infty} $ to $ H^{p, \infty}_b $ was demonstrated for

    $ \frac{n}{n+\delta}<p\leq 1. $



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