Working in the frame of variable bounded variation spaces in the sense of Wiener, introduced by Castillo, Merentes, and Rafeiro, we prove convergence in variable variation by means of the classical convolution integral operators. In the proposed approach, a crucial step is the convergence of the variable modulus of smoothness for absolutely continuous functions. Several preliminary properties of the variable p(·)-variation are also presented.

Convolution Integral Operators in Variable Bounded Variation Spaces

Angeloni L.
;
2023

Abstract

Working in the frame of variable bounded variation spaces in the sense of Wiener, introduced by Castillo, Merentes, and Rafeiro, we prove convergence in variable variation by means of the classical convolution integral operators. In the proposed approach, a crucial step is the convergence of the variable modulus of smoothness for absolutely continuous functions. Several preliminary properties of the variable p(·)-variation are also presented.
2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1541720
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