On the Predual of a Morrey–Lorentz Space and Its Applications to the Linear Calderón–Zygmund Operators
Frontiers of Mathematics(2024)
Abstract
Our main purpose in this paper is to construct a predual of Morrey–Lorentz space via the block spaces, defined in [Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 1999, 28(1): 31–40]. As a direct application of duality, we obtain the Morrey–Lorentz boundedness of linear Calderón–Zygmund operators. Moreover, we study a weak Hardy factorization in terms of linear Calderón–Zygmund operators in Morrey–Lorentz spaces. As a consequence of this result, we obtain a characterization of functions in BMO(ℝn) through the boundedness of commutator [b, T], where T is a homogeneous Calderón–Zygmund operator. Finally, we prove a Morrey–Lorentz compactness characterization of [b, T]. Precisely, [b, T] is a compact operator on Morrey–Lorentz spaces if and only if b ∈ CMO(ℝn).
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Key words
Morrey–Lorentz space,block space,weak Hardy factorization,linear Calderón–Zygmund operator,42B35,42B20,46E30,46A20
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