On moduli of smoothness and Fourier multipliers in $L_p, 0 < p < 1$
We obtain the theorem on the relationship between a modulus of smoothness and the best approximation in L p , 0 < p < 1,
and theorems on the extension of functions with the preservation of the modulus of smoothness in L p , 0 < p < 1.
In addition, we present a complete description of multipliers of periodic functions in the spaces L p , 0 < p < 1.
English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 9, pp 1364-1384.
Citation Example: Kolomoitsev Yu. S. On moduli of smoothness and Fourier multipliers in $L_p, 0 < p < 1$ // Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1221–1238.