Non-homogeneous T1 theorem for bi-parameter singular integrals
Tuomas Hyt\"onen, Henri Martikainen
TL;DR
This paper establishes a non-homogeneous T1 theorem for bi-parameter singular integrals, extending classical results to more general settings with non-uniform measures.
Contribution
It introduces a non-homogeneous T1 theorem for bi-parameter singular integrals and explores related non-homogeneous Journe's lemma and product BMO theory.
Findings
Proved a non-homogeneous T1 theorem for bi-parameter singular integrals.
Extended Journe's lemma to non-homogeneous settings.
Developed product BMO theory in the non-homogeneous context.
Abstract
We prove a non-homogeneous T1 theorem for certain bi-parameter singular integral operators. Moreover, we discuss the related non-homogeneous Journe's lemma and product BMO theory.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Banach Space Theory · Mathematical Analysis and Transform Methods