Endpoint theory for the compactness of commutators

2023/09/19 by Wang, Dinghuai, Hu, Xi, Qi, Shuai
#46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B50 #Secondary 42B20

paper · doi:10.48550/arxiv.2309.10343

Abstract

In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of commutators at the endpoint. The paper provides a comprehensive study of the compactness properties of commutators of Calderón-Zygmund operators in Hardy and L¹(ℝⁿ) type spaces. Additionally, we provide factorization theorems for Hardy spaces in terms of singular integral operators in the L¹(ℝⁿ) space.

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