Bourgain-Morrey-Lorentz spaces and operators on them
Tengfei Bai, Pengfei Guo, Jingshi Xu

TL;DR
This paper introduces Bourgain-Morrey-Lorentz spaces, explores their duality and operator boundedness, and characterizes BMO functions via commutator boundedness and compactness within these spaces.
Contribution
It defines Bourgain-Morrey-Lorentz spaces, establishes duality with block spaces, and analyzes boundedness and compactness of classical operators on these spaces.
Findings
Boundedness of Hardy-Littlewood maximal, sharp maximal, Calderón-Zygmund, and fractional integral operators.
Characterization of BMO functions via commutator boundedness.
Compactness of commutators characterized by limits of smooth functions in BMO.
Abstract
We introduce Bourgain-Morrey-Lorentz spaces and give a description of the predual of Bourgain-Morrey-Lorentz spaces via the block spaces. As an application of duality, we obtain the boundedness of Hardy-Littlewood maximal operator, sharp maximal operator, Calder\'on-Zygmund operator, fractional integral operator, commutator on Bourgain-Morrey-Lorentz spaces. Moreover, we obtain a weak Hardy factorization terms of Calder\'on-Zygmund operator in Bourgain-Morrey-Lorentz spaces. Using this result, we obtain a characterization of functions in (the functions of ``bounded mean oscillation'') via the boundedness of commutators generated by them and a homogeneous Calder\'on-Zygmund operator. In the last, we show that the commutator generated by a function and a homogeneous Calder\'on-Zygmund operator is a compact operator on Bourgain-Morrey-Lorentz spaces if and only if is the…
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · advanced mathematical theories · Mathematical Analysis and Transform Methods
