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Functions of Bounded (p(⋅), 2)-Variation in De la Vallée Poussin-Wiener’s Sense with Variable Exponent

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DOI: 10.4236/apm.2017.79033    325 Downloads   512 Views  


In this paper we establish the notion of the space of bounded  (p(⋅), 2)variation in De la Vallée Poussin-Wiener’s sense with variable exponent. We show some properties of this space and we show that any uniformly bounded composition operator that maps this space into itself necessarily satisfies the so-called Matkowski’s conditions.

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The authors declare no conflicts of interest.

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Mejía, O. , Silvestre, P. and Valera-López, M. (2017) Functions of Bounded (p(⋅), 2)-Variation in De la Vallée Poussin-Wiener’s Sense with Variable Exponent. Advances in Pure Mathematics, 7, 507-532. doi: 10.4236/apm.2017.79033.


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