An endpoint estimate for the maximal Calderón commutator with rough kernel

2024/03/23 by Hu, Guoen, Lai, Xudong, Tao, Xiangxing +1
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.15758

Abstract

In this paper, the authors consider the endpoint estimates for the maximal Calderón commutator defined by T_{Ω, a}^*f(x)=sup_εgt;0|∫_|x-y|gt;ε\fracΩ(x-y)|x-y|^d+1 (a(x)-a(y))f(y)dy|, where Ω is homogeneous of degree zero, integrable on S^d-1 and has vanishing moment of order one, a be a function on ℝ^d such that ∇ a∈ L^∞(ℝ^d). The authors prove that if Ω∈ Llog L(S^d-1), then T^*_{Ω, a} satisfies an endpoint estimate of Lloglog L type.

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