A Characterization of Absolute Continuity by means of Mellin Integral Operators

被引：13

作者：

Angeloni, Laura ^{[1
]}

Vinti, Gianluca ^{[1
]}

机构：

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

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2015年 / 34卷 / 03期

关键词：

Mellin integral operators; absolute continuity; multidimensional variation; convergence in variation; DILATIONALLY INVARIANT TRANSFORMS; EXPONENTIAL-SAMPLING METHOD; CONVERGENCE; APPROXIMATION; RESPECT; LAPLACE;

D O I：

10.4171/ZAA/1543

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the case of classical convolution operators, an important characterization of absolute continuity is given in terms of convergence in variation. In this paper we will study this problem for Mellin integral operators, proving analogous characterizations in the frame of the classical BV-spaces, both in the one-dimensional and in the multidimensional setting.

引用

页码：343 / 356

页数：14

共 32 条

[1]

Angeloni L, 2011, B UNIONE MAT ITAL 9, V4, P79

[2]

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

[3]

Angeloni L., 2014, NEW PERSPECTIVES APP, P299

[4] Convergence in variation and a characterization of the absolute continuity [J].