Realization functionals and description of a modulus of smoothness in variable exponent Lebesgue spaces

S. S. Volosivets

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2022), pp. 13-25.

Résumé

In variable exponent Lebesgue spaces the equivalence between generalized modulus of smoothness defined with help of one-sided Steklov means and realization functionals using Riesz-Zygmund and Euler means is established. The description of a class of functions which are equivalent to a generalized modulus of smoothness of order $r\in\mathbb N$ is given.

Détail

Mots-clés : variable exponent Lebesgue space
Keywords: generalized modulus of smoothness, $K$-functional, realization functional.

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