Multivariate Approximation Theorems in Weighted Lorentz Spaces

Abstract

We consider trigonometric polynomial approximation problems in the multivariate weighted Lorentz spaces. In particular, we prove direct and converse theorems for trigonometric approximation in the multivariate weighted Lorentz spaces with Ap-weights.Mathematics Subject Classification. 41A17, 41A25, 42A10, 46E30.

Generalized derivatives and approximation in weighted Lorentz spaces

“…Also there are many results of the approximation theory obtained in these spaces. Especially, approximation by trigonometric polynomials in the weighted Lorentz spaces was considered in the papers [3,4,15,29,30]. But these papers do not have results about the approximation properties of (ψ, β)-derivatives.…”

Approximation in weighted Lorentz spaces On moduli of smoothness and approximation by trigonometric polynomials in weighted Lorentz spaces

“…The problems of approximation theory in the weighted and nonweighted Lorentz space have been investigated in [1], [21], [35] and [37]. The approximation problems by trigonometric polynomials in dierent spaces have been investigated by several authors (see, for example, [2][3][4][5], [7], [9], [11], [13][14][15][16][17][18][19], [22], [23], [28][29][30], [33] and [34]).…”