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Characterization of inclusion among Riesz−Medvedev variation spaces

Aziz W., Ereú T.

Commentationes Mathematicae

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2016

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Vol 56, No. 2

225--237

EN

We present a characterization of inclusion among Riesz−Medvedev bounded variation spaces, i.e., we shall present necessary and sufficient conditions for the Young functions φ1 and φ2 so that RVφ1[a,b]⊂RVφ2[a,b] or RV∗φ1[a,b]⊂RV∗φ2[a,b] .

2

Remarks on uniformly bounded composition operator acting between Banach spaces of functions of two variables of bounded schramm Φ-variation

Ereú T., Merentes N., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2013

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Vol. 18

19--27

EN

In this paper we prove that if the composition operator H of generator h : Ib a × C → Y (X is a real normed space, Y is a real Banach space, C is a convex cone in X and Ib a ⸦ R2) maps Φ1 BV (Ib a, C) into Φ2 BV (Ib a, Y) and is uniformly bounded, then the left-left regularization h* of h is an affine function in the third variable.

3

Uniformly continuous composition operator in the space of functions of two variables of Bounded ɸ-variation in the sense of Schramm

Aziz W., Ereú T., Merentes N., Sanchez J. L., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2012

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Vol. 17

7-16

EN

We prove in this paper that if the composition operator H, generated by a function h : I b a x C(Iba) Y , maps ɸBV (Iba ,C) into ɸ2 BV (Iba , Y ) and is uniformly continuous, then the left-left regularization h* of h is an affine function with respect to the third variable.

4

Uniformly bounded set-valued composition operators in the spaces of functions of bounded variation in the sense of Schramm

Ereú T., Merentes N., Sanchez J. L., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2012

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Vol. 17

37-47

EN

We prove that, under some general assumptions, the one-sided regularizations of the generator of any uniformly bounded set-valued composition operator, acting in the spaces of functions of bounded variation in the sense of Schramm with nonempty bounded closed and convex values is an aﬃne function. As a special case, we obtain an earlier result ([15]).

5

Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Schramm

Ereú T., Sánchez J. L., Merentes N., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2011

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Vol. 16

23--32

EN

We show that the one-sided regularizations of the generator of any uniformly continuous set-valued Nemytskij operator, acting between the spaces of functions of bounded variation in the sense of Schramm, is an affine function. Results along these lines extend the study [1].