Commutators on Spaces of Homogeneous Type in Generalized Block Spaces

Author:

Dung Tran Tri,Dao Nguyen Anh,Duong Xuan Thinh,Nghia Le Trung

Abstract

AbstractIn this paper, we are interested in studying a generalized block space (denoted as $$\textbf{B}^{p,r}_\varphi $$ B φ p , r ) on a space of homogeneous type. We show that this space is the predual of certain generalized Morrey–Lorentz space. By duality, we obtain the $$\textbf{B}^{p,r}_\varphi $$ B φ p , r -bound of operators of Calderón–Zygmund type. In addition, we prove a weak Hardy factorization in terms of commutators of integral operator of Calderón–Zygmund type in block spaces. Thanks to the Hardy factorization result, we obtain a characterization of functions in $$\textrm{BMO}$$ BMO via the boundedness of commutators of homogeneous linear Calderón–Zygmund operators in the generalized block space (resp. the generalized Morrey–Lorentz space). Finally, we study a compactness characterization of commutators of Calderón–Zygmund type in generalized Morrey–Lorentz spaces.

Funder

Australian Research Council

Macquarie University

Publisher

Springer Science and Business Media LLC

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