On moduli of smoothness and Fourier multipliers in \(L_p,0<p<1\). (Russian, English) Zbl 1150.41019
Ukr. Mat. Zh. 59, No. 9, 1221-1238 (2007); translation in Ukr. Math. J. 59, No. 9, 1364-1384 (2007).
Summary: 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 \(L_p,0<p<1\).
MSC:
| 41A50 | Best approximation, Chebyshev systems |
