Weighted vector-valued estimates for a non-standard Calderón-Zygmund operator

2016/02/25 by Hu, Guoen
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1602.07830

Abstract

In this paper, the author considers the weighted vector-valued estimate for the operator defined by T_Af(x)=\rm p. v.∫_ℝⁿ\fracΩ(x-y)|x-y|ⁿ⁺¹(A(x)-A(y)-∇ A(y))f(y)\rm dy, and the corresponding maximal operator T_A^*, where Ω is homogeneous of degree zero, has vanishing moment of order one, A is a function in ℝⁿ such that ∇ A∈ \rm BMO(ℝⁿ). By a pointwise estimate for ‖\T_Af_k(x)\‖_l^q and the weighted L^p estimates for the sparse operator A_{S, L(log L)^β}f(x)=∑_Q\inS‖f‖_{L(log L)^β, Q}χ_Q(x) , the author establishes some weak and endpoint quantitative weighted vector-valued estimates for T_A and T_A^*.

Related

• Vector-valued operators, optimal weighted estimates and the C_p condition
• Sharp weighted estimates for multi-frequency Calderón-Zygmund operators
• Convex body domination and weighted estimates with matrix weights
• Weighted norm estimates of noncommutative Calderón-Zygmund operators
• Sharp weighted estimates for multi-linear Calder 'on-Zygmund operators\n on non-homogeneous spaces