Geodesic
Realization functionals and description of a modulus of smoothness in variable exponent Lebesgue spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2022), pp. 13-25

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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.
Mots-clés : variable exponent Lebesgue space
Keywords: generalized modulus of smoothness, $K$-functional, realization functional. 
@article{IVM_2022_6_a1,
     author = {S. S. Volosivets},
     title = {Realization functionals and description of a modulus of smoothness in variable exponent {Lebesgue} spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {13--25},
     publisher = {mathdoc},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_6_a1/}
}
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S. S. Volosivets. Realization functionals and description of a modulus of smoothness in variable exponent Lebesgue spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2022), pp. 13-25. http://geodesic.mathdoc.fr/item/IVM_2022_6_a1/