ACTA issues

Approximation of functions of several variables by linear methods in the space $S^p$

Viktor V. Savchuk, Andriy L. Shidlich

Acta Sci. Math. (Szeged) 80:3-4(2014), 477-489

Abstract. In the spaces $S^p$ of functions of several variables, $2\pi $-periodic in each variable, we study the approximative properties of operators $A^\triangle _\varrho,r$ and $P^\triangle _\varrho,s$, which generate two summation methods of multiple Fourier series on triangular regions. In particular, in the terms of approximation estimates of these operators, we give a constructive description of classes of functions, whose generalized derivatives belong to the classes $S^pH_\omega $.

DOI: 10.14232/actasm-012-837-8

AMS Subject Classification (1991): 42B05, 26B30, 26B35

Keyword(s): space $S^p$, classes $H_\omega $, linear methods

Received October 30, 2012. (Registered under 87/2012.)