TL;DR
This paper establishes a bi-parameter T(b) theorem for tensor product pseudo-accretive functions, advancing the understanding of boundedness in product spaces and analyzing associated bi-parameter paraproducts.
Contribution
It introduces a bi-parameter T(b) theorem for tensor product pseudo-accretive functions and explores L^2 boundedness of related bi-parameter paraproducts.
Findings
Proved a bi-parameter T(b) theorem for tensor product pseudo-accretive functions
Analyzed L^2 boundedness of b-adapted bi-parameter paraproducts
Extended the theory of T(b) theorems to product space settings
Abstract
The main result of this paper is a bi-parameter T(b) theorem for the case that b is a tensor product of two pseudo-accretive functions. In the proof, we also discuss the L^2 boundedness of different types of the b-adapted bi-parameter paraproducts.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Banach Space Theory · Mathematical Analysis and Transform Methods