A simple proof of the sharp weighted estimate for Calderon-Zygmund\n operators on homogeneous spaces

2012/06/12 by Theresa C. Anderson, Anderson, Theresa C., Armen Vagharshakyan +1 · 1 citation
Mathematics · Medicine · #42B20 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Soft tissue tumor case studies

paper · pdf · doi:10.48550/arxiv.1206.2489

openalex publication_date 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here we show that Lerner's method of local mean oscillation gives a simple\nproof of the A₂ conjecture for spaces of homogeneous type: that is, the\nlinear dependence on the A₂ norm for weighted L² Calderon-Zygmund\noperator estimates. In the Euclidean case, the result is due to Hyt "onen,\nand for geometrically doubling spaces, Nazarov, Rezinikov, and Volberg obtained\nthe linear bound.\n

Citations

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

Cited by

• The maximal function on spaces of homogeneous type, or adjacent dyadic cubes do good

Related

• Sharp weighted estimates for multi-linear Calder 'on-Zygmund operators\n on non-homogeneous spaces
• Calderón-Zygmund operators and commutators in spaces of homogeneous type: weighted inequalities
• The sharp weighted bound for general Calderon-Zygmund operators
• On A₂ conjecture and corona decomposition of weights
• The Linear Bound in A₂ for Calderón-Zygmund Operators: A Survey