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2 2010

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On composition operator in the algebra of functions of two variables with bounded total Φ-variation in Schramm sense

Ereu T., Merentes N., Rzepka B., Sanchez J. L.

Journal of Mathematics and Applications

2010

Vol. 33

35-50

In this paper we consider the so called composition operator being a self-mapping of the Banach algebra of the function of two variables with bounded total Φ-variation in the Schramm sense. The main result of the paper characterizes the composition operator mentioned above which has a generating function being Lipschitzian with respect to the second variable. The basic tool used in our considerations is the concept of the left-left regularization.

A Representation Theorem for '-Bounded Variation of Functions in the Sense of Riesz

Aziz W., Leiva H., Merentes N., Rzepka B.

Commentationes Mathematicae

2010

Vol. 50, [Z] 2

109-120

In this paper we extend the well known Riesz lemma to the class of bounded φ-variation functions in the sense of Riesz defined on a rectangle [...].This concept was introduced in [2], where the authors proved that the space [...] of such functions is a Banach Algebra. Moreover, they characterized also the Nemytskii operator acting in this space. Thus our result creates a continuation of the paper [2].