Abstract
We prove the equivalence of special moduli of smoothness and K-functionals of fractional order in the space H p , p > 0. As applications, we obtain an analog of the Hardy–Littlewood theorem and the sharp estimates of the rate of approximation of functions by generalized Bochner–Riesz means.
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Translated from Russian by V. V. Kukhtin
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 8, No. 3, pp. 421–446, July–August, 2011.
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Kolomoitsev, Y.S. On moduli of smoothness and K-functionals of fractional order in the Hardy spaces. J Math Sci 181, 78–97 (2012). https://doi.org/10.1007/s10958-012-0677-7
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DOI: https://doi.org/10.1007/s10958-012-0677-7