BI-PARAMETER LITTLEWOOD-PALEY OPERATORS WITH UPPER DOUBLING MEASURES

摘要

Let μ = μ_(n1) x μ_(n2), where μ_(n1) and μ_(n2) are upper doubling measures on R~(n1) and R~(n2), respectively. Let the pseudo-accretive function b = b_1 ?? b_2 satisfy a bi-parameter Carleson condition. In this paper, we established the L2(p) bounded-ness of non-homogeneous Littlewood-Paley g_λ-function with non-convolution type kernels on product spaces. This was mainly done by means of dyadic analysis and non-homogenous methods. The result is new even in the setting of Lebesgue measures.