A₁ theory of weights for rough homogeneous singular integrals and commutators

2016/07/21 by Carlos Pérez, Perez, C., Israel P. Rivera-Rı́os +3
Mathematics · #42B20 #42B25 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · doi:10.48550/arxiv.1607.06432

openalex publication_date 2016/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Quantitative A₁-A_∞ estimates for rough homogeneous singular integrals T_Ω and commutators of BMO symbols and T_Ω are obtained. In particular the following estimates are proved: % ‖T_Ω‖_L^p(w)≤ c_n,p‖Ω‖_L^∞ [w]_A1^(1)/(p) [w]_A_∞^1+(1)/(p')‖f‖_L^p(w) % and % ‖ [b,T_Ω]f‖_L^p(w)≤ c_n,p‖b‖_BMO‖Ω‖_L^∞ [w]_A1^(1)/(p)[w]_A_∞^2+(1)/(p')‖f‖_L^p(w), % for 1

Citations

• Weighted inequalities for the dyadic square function without dyadic A∞
• Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular
• A Bellman function counterexample to the A₁ conjecture: the blow-up of the weak norm estimates of weighted singular operators
• Some Maximal Inequalities

Related

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