On approximation in Weighted Orlicz spaces

Abstract

ABSTRACT. An inverse theorem of the trigonometric approximation theory in Weighted Orlicz spaces is proved and the constructive characterization of the generalized Lipschitz classes defined in these spaces is obtained.

Approximation of functions belonging to the weighted L(a, M, omega)-class by trigonometric polynomials

“…The results obtained in this work, are generalization of the results [13] and [42] to more general summability and weighted Orlicz spaces. Similar problems about approximations of the functions by trigonometric polynomials in the different spaces have been investigated by several authors (see, for example, [2], [3], [10][11][12][13][14][15][16][17][18][19][20][21], [23][24][25][26], [33][34][35][36][37][38] , [40] and [42][43][44][45]).…”

Approximation by Nörlund and Riesz means in weighted Lebesgue space with variable exponent

“…In [11] under the some conditions related with the sequence (p n ) 1 n=0 Chandra proved satisfactory results about approximation by the N n (f ) and R n (f ) means in in classical Lipschitz classes where 1 p < 1 and 0 < 1. Guven carried and extended the results obtained in [11] to weighted Lipschitz classes where 1 < p < 1 (see, [13,14]). In the Lebesgue space with variable exponent space Guven and Isra…lov investigated the approximation properties of N n (f ) and R n (f ) means for Lipschitz classes in [15].…”

Multivariate Approximation Theorems in Weighted Lorentz Spaces

“…These results can be found in the monographs [7,21] for Lebesgue L p spaces. In the weighted Lebesgue and Lorentz spaces with Muckenhoupt A p -weights, some results were obtained in [1][2][3][10][11][12][13][14][15][16][17]22,23].…”