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On moduli of smoothness and Fourier multipliers in L p , 0 < p< 1

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Abstract

We prove a theorem on the relationship between the modulus of smoothness and the best approximation in L p , 0 < p < 1, and theorems on the extension of functions with preservation of the modulus of smoothness in L p , 0 < p < 1. We also give a complete description of multipliers of periodic functions in the spaces L p , 0 < p < 1.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1221–1238, September, 2007.

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Kolomoitsev, Y.S. On moduli of smoothness and Fourier multipliers in L p , 0 < p< 1. Ukr Math J 59, 1364–1384 (2007). https://doi.org/10.1007/s11253-007-0092-2

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  • DOI: https://doi.org/10.1007/s11253-007-0092-2

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