Derivatives of Trigonometric Polynomials and Converse Theorem of the Constructive Theory of functions in Morrey Spaces

Abstract

Let T denote the interval [-0, 2?]. In this work the relationship between the modulus of smoothness of derivatives of a function and the best approximation in Morrey space Lp,? (T), 0 < ? ? 2, 1 < p < 8, have been investigated. In addition, the theorems related to the derivatives of trigonometric polynomials in Morrey space Lp,? (T), 0 < ? ? 2, 1 < p < ?, are proved. © 2019, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.