MAXIMAL BILINEAR CALDERON ZYGMUND OPERATORS OF TYPE ω(t) ON NON-HOMOGENEOUS SPACE

作者：Zheng, Taotao^*; Wang, Zheng; Xiao, Weiliang

来源：Annals of Functional Analysis, 2015, 6(4): 134-154.

DOI：10.15352/afa/06-4-134

• Bilinear Calderon-Zygmund operator
• sharp maximal operator
• non homogeneous space
• upper doubling measures
• weight

Let (X, d, mu) be a geometrically doubling metric space and assume that the measure mu satisfies the upper doubling condition. In this paper, the authors, by invoking a Cotlar type inequality, show that the maximal bilinear Calderon-Zygmund operators of type omega(t) is bounded from L-P1 x L-P2(mu) into L-P (mu) for any p(i) is an element of (1, infinity] and bounded from L-P1 (mu) x L-P2(mu) into L-P,L-infinity (mu) for p(1) = 1 or p(2) = 1, where p is an element of [1/2, infinity), 1/p(1) + 1/p(2) = 1/p. Moreover, if w = (w(1), w(2)) belongs to the weight class A(p)(rho)(mu), using the John-stromberg maximal operator and the John-stromberg sharp maximal operator, the authors obtain a weighted weak type estimate L-p1 (w(1)) x L-P2(w(2)) -> LP,infinity(v (w) over bar) for the maximal bilinear Calderon Zygmund operators of type w(t). By weakening the assumption of w E Dini(1/2) into w is an element of Dini(1), the results obtained in this paper are substantial improvements and extensions of some known results, even on Euclidean spaces R-n

• 出版日期2015
• 单位浙江科技学院; 浙江大学