Approximation by trigonometric polynomials in weighted Morrey spaces
Z. Cakir, C. Aykol, D. Soylemez, A. Serbetci
In this paper we investigate the best approximation by trigonometric polynomials in weighted
Morrey spaces $\mathcal{M}_{p,\lambda}(I_{0},w)$, where the weight
function $w$ is in the Muckenhoupt class $A_{p}(I_{0})$ with $1 < p < \infty$
and $I_{0}=[0, 2\pi]$. We prove the direct and inverse theorems of
approximation by trigonometric polynomials in the spaces
$\mathcal{\widetilde{M}}_{p,\lambda}(I_{0},w)$ the closure of $C^{\infty
}(I_{0})$ in $\mathcal{M}_{p,\lambda}(I_{0},w)$. We give
the characterization of $K$functionals in terms of the modulus of smoothness
and obtain the Bernstein type inequality for trigonometric polynomials in the
spaces $\mathcal{M}_{p,\lambda}(I_{0},w)$.
Tbilisi Mathematical Journal, Vol. 13(1) (2020), pp. 123138
