用Mellin积分算子描述绝对连续性

Pub Date : 2015-07-08 DOI:10.4171/ZAA/1543

L. Angeloni, G. Vinti

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引用次数: 15

摘要

对于经典卷积算子，从变分收敛的角度给出了绝对连续性的一个重要特征。在本文中，我们将研究Mellin积分算子的这一问题，证明在一维和多维情况下经典BV -空间框架中的类似刻画。

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A Characterization of Absolute Continuity by means of Mellin Integral Operators

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.

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