A concept of absolute continuity and its characterization in terms of convergence in variation

被引：6

作者：

Angeloni, Laura ^{[1
]}

Vinti, Gianluca ^{[1
]}

机构：

[1] Univ Perugia, Dipartimento Matemat & Informat, Via Vanvitelli 1, I-06123 Perugia, Italy

来源：

MATHEMATISCHE NACHRICHTEN | 2016年 / 289卷 / 16期

关键词：

phi-absolute continuity; multidimensional phi-variation; Mellin operators; convergence in variation; LINEAR INTEGRAL-OPERATORS; PHI-VARIATION; APPROXIMATION;

D O I：

10.1002/mana.201500271

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the notion of phi-absolute continuity, providing several equivalent definitions, and we prove a characterization of the space of phi-absolutely continuous functions in terms of convergence in variation for a family of Mellin integral operators in the multidimensional setting.

引用

页码：1986 / 1994

页数：9

共 36 条

[1]

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[2]

Angeloni L, 2011, BOLL UNIONE MAT ITAL, V4, P79

[3]

Angeloni L., 2013, Commun. Appl. Nonlinear Anal, V20, P1

[4] A Characterization of Absolute Continuity by means of Mellin Integral Operators [J].