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

Abstract

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.