lp(Zd)-estimates for discrete operators of Radon type: variational estimates

• 成果类型: Article
• 署名作者: Mirek, Mariusz; Stein, Elias M.; Trojan, Bartosz
• 署名单位: Institute for Advanced Study - USA; University of Wroclaw; Princeton University; Wroclaw University of Science & Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0718-4
• 发表日期: 2017
• 页码: 665-748
• 关键词: p-variation

摘要

We prove l(p)(Z(d)) bounds for p is an element of(1,infinity) of r-variations r is an element of(2,infinity) for discrete averaging operators and truncated singular integrals of Radon type. We shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of p and r which coincide with the ranges of their continuous counterparts.