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On the total variation for functions of several variables and a multidimensional analog of Helly's selection principle

A. S. Leonov

Moscow Engineering Physics Institute (State University)

Abstract: We introduce the new notion of total variation for the Hardy class of functions of several variables and state various properties, similar to those in the one-dimensional case, for functions belonging to this class. In particular, we prove a precise version of Helly's selection principle for this class.

UDC: 517.397

Received: 22.04.1996

DOI: 10.4213/mzm1249

 English version: Mathematical Notes, 1998, 63:1, 61–71

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