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
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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