A note on sharp weighted bound for Haar shift and multiplier
Chih-Chieh Hung, Chun-Yen Shen
TL;DR
This paper offers elementary proofs for the sharp weighted bounds of Haar shifts and multipliers, simplifying previous complex arguments using classical harmonic analysis tools.
Contribution
It introduces simplified, elementary proofs for the sharp weighted A_2 bounds in Haar shift and multiplier operators, building on prior advanced work.
Findings
Elementary proofs for sharp weighted bounds
Use of weighted square function estimate and Carleson embedding
Simplification of existing complex proofs
Abstract
We provide elementary proofs for the terms that are left in the work of Kelly Bickel, Sandra Pott, Maria C. Reguera, Eric T. Sawyer, Brett D. Wick who proved the sharp weighted bound for Haar shifts and Haar multiplier. Our proofs use weighted square function estimate, Carleson embedding and Wilson's system.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Holomorphic and Operator Theory · Advanced Banach Space Theory