A survey on composition operators on some function spaces

In this paper, we obtained a necessary and sufficient condition for the embedding H?q([0,1])? IBVqp([0,1]), where IBVq p denotes the set of functions of bounded q-integral p-variation. Additionally, the conditions for the composition and superposition operators were provided to map the space H?q([0,1]) into itself, by which these operators were bounded. Finally, we applied these results to examine the existence and uniqueness of solutions to Hammerstein integral equations in the space of H?q([0,1]).

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Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces

Angeloni¹,

Çetin²,

Costarelli³

et al. 2021

Constructive Mathematical Analysis

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In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.

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A survey on composition operators on some function spaces

Abstract: We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.

Cited by 3 publications

References 23 publications

Expansivity property for composition operators on the Orlicz–Lorentz space

Expansivity property for composition operators on the Orlicz–Lorentz space

On the superposition operator in the space of functions of Hωq ([0,1])

Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces

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