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

Abstract

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. $

Keywords

• weak hardy space
• para-accretive function
• atomic decomposition
• calderón-zygmund operator