Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces - Cakir, Z.; Aykol, C.; Guliyev, V.S.; Serbetci, A. (Carpathian Mathematical Publications, 2021)
In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces ${\mathcal{M}}_{p(·),λ(·)}(I_{0},w)$, where $w$ is a weight function in the Muckenhoupt $A_{p(·)}(I_{0})$ class. We get a characterization of $K$-functionals in terms of the modulus of smoothness in the spaces ${\mathcal{M}}_{p(·),λ(·)}(I_{0},w)$. Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces ${\mathcal{\widetilde{M}}}_{p(·),λ(·)}(I_{0},w),$ the closure of the set of all trigonometric polynomials in ${\mathcal{M}}_{p(·),λ(·)}(I_{0},w)$.