Regularity of discrete multisublinear fractional maximal functions

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（8）
• 页码范围: 1461-1476
• 页数: 16页
• 语种: 英文
• DOI: 10.1007/s11425-016-9011-2

摘要

We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l1(Zd) × l1(Zd) × … × l1(Zd) to BV(Zd),where BV(Zd) is the set of functions of bounded variation defined on Zd.Moreover,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given.As applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.