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The characterisation of $BMO$ via commutators in variable Lebesgue spaces on stratified groups

Dongli Liu|Jian Tan|Jiman Zhao
대한수학회 (The Korean Mathematical Society)|2022.05|대한수학회보 (Bulletin of the KMS)|제59권 제3호|pp. 547-566|DOI 10.4134/BKMS.b201019

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참고문헌

키워드

Bilinear Calder\'{o}n-Zygmund operatorsvariable Lebesgue spacesstratified groups
주제분류수학

초록

Let $T$ be a bilinear Calder\'{o}n-Zygmund operator, $$b\in \cup_{q>1}L_{loc}^{q}(G).$$ We firstly obtain a constructive proof of the weak factorisation of Hardy spaces. Then we establish the characterization of $BMO$ spaces by the boundedness of the commutator $[b, T]_{j}$ in variable Lebesgue spaces.

Abstract

Let $T$ be a bilinear Calder\'{o}n-Zygmund operator, $$b\in \cup_{q>1}L_{loc}^{q}(G).$$ We firstly obtain a constructive proof of the weak factorisation of Hardy spaces. Then we establish the characterization of $BMO$ spaces by the boundedness of the commutator $[b, T]_{j}$ in variable Lebesgue spaces.

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