Two weight inequalities for individual Haar multipliers and other well localized operators
Fedor Nazarov, Sergei Treil, Alexander Volberg
TL;DR
This paper establishes that Sawyer type conditions are sufficient for two-weight boundedness of Haar multipliers, Haar shifts, and other well-localized operators, advancing understanding of weighted inequalities in harmonic analysis.
Contribution
It proves that Sawyer type conditions characterize two-weight boundedness for Haar multipliers and related operators, extending previous results to a broader class of well-localized operators.
Findings
Sawyer type conditions are sufficient for two-weight boundedness.
Results apply to Haar multipliers, Haar shifts, and well-localized operators.
Advances understanding of weighted inequalities in harmonic analysis.
Abstract
In this paper we are proving that Sawyer type condition for boundedness work for the two weight estimates of individual Haar multipliers, as well as for the Haar shift and other "well localized" operators.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Holomorphic and Operator Theory · Differential Equations and Boundary Problems