Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces

  • Z. Cakir Department of Mathematics, Ankara University, Ankara, Turkey
  • C. Aykol Department of Mathematics, Ankara University, Ankara, Turkey
  • V.S. Guliyev Baku State University, Baku, Azerbaijan
  • A. Serbetci Department of Mathematics, Ankara University, Ankara, Turkey
Keywords: variable exponent weighted Morrey space, best approximation, trigonometric polynomial, direct and inverse theorem
Published online: 2021-12-29

Abstract


In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$, where $w$ is a weight function in the Muckenhoupt $A_{p(\cdot)}(I_{0})$ class. We get a characterization of $K$-functionals in terms of the modulus of smoothness in the spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$. Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces ${\mathcal{\widetilde{M}}}_{p(\cdot),\lambda(\cdot)}(I_{0},w),$ the closure of the set of all trigonometric polynomials in ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$.

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How to Cite
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Cakir Z., Aykol C., Guliyev V., Serbetci A. Approximation by Trigonometric Polynomials in the Variable Exponent Weighted Morrey Spaces. Carpathian Math. Publ. 2021, 13 (3), 750-763.