Convolution Integral Operators in Variable Bounded Variation Spaces
Copyright policy )Convolution Integral Operators in Variable Bounded Variation Spaces
AbstractWorking 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$$p(\cdot )$$p(·)-variation are also presented.
- Central University of Venezuela Venezuela
- University of Perugia Italy
Integral operators, convolution integral operators, modulus of smoothness, Bounded variation spaces with variable exponent, convergence in variable variation, Convolution integral operators, modulus of smoothness, Functions of bounded variation, generalizations, Approximation by operators (in particular, by integral operators), bounded variation spaces with variable exponent, convergence in variable variation
Integral operators, convolution integral operators, modulus of smoothness, Bounded variation spaces with variable exponent, convergence in variable variation, Convolution integral operators, modulus of smoothness, Functions of bounded variation, generalizations, Approximation by operators (in particular, by integral operators), bounded variation spaces with variable exponent, convergence in variable variation
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