Weak and Strong-type estimates for Haar Shift Operators: Sharp power on the A_p characteristic

2009/11/03 by Tuomas Hytönen, Hytönen, Tuomas P., Michael T. Lacey +5 · 2 citations
Mathematics · #42B20 #42C40 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0911.0713

openalex publication_date 2009/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As a corollary to our main result we deduce sharp A_p inequalities for T being either the Hilbert transform in dimension d=1, the Beurling transform in dimension d=2, or a Riesz transform in any dimension d≥ 2. For T_∗ the maximal truncations of these operators, we prove the sharp A_p weighted weak and strong-type L ^p (w) inequalities, for all 1

Citations

• Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular

Cited by

• The sharp weighted bound for general Calderon-Zygmund operators
• Weak and Strong type A_p Estimates for Calderón-Zygmund Operators

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