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

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Hacettepe Journal of Mathematics and Statistics
Volume:45 Issue:6
On moduli of smoothness and approximation by trigonometric polynomials in weighted Lorentz spaces

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

Authors : Sadulla Z JAFAROV

Pages : 1675-1684

View : 55 | Download : 10

Publication Date : 2016-12-01

Article Type : Research Paper

Abstract :We investigate the approximation properties of the functions by trigonometric polynomials in weighted Lorentz spaces with weights satisfying so called Muckenhoupt`s Ap condition. Relations between moduli of smoothness of the derivatives of the functions and those of the functions itself are studied. In weighted Lorentz spaces we also prove a theorem on the relationship between the derivatives of a polynomial of best approximation and the best approximation of the function. Moreover, we study relationship between modulus of smoothness of the function and its de la Vallée-Poussin sums in these spaces.
Keywords : moduli of smoothness, weighted Lorentz spaces, Muckenhoupt weight, trigonometric approximation, best approximation

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