Linear methods of approximation in weighted Lebesgue spaces with variable exponent

Year 2021, Volume: 50 Issue: 3, 744 - 753, 07.06.2021

Ahmet Testici , Daniyal M. İsrafilzade

https://doi.org/10.15672/hujms.798028

Abstract

Some estimations in below for the deviations conducted by the Zygmund means and by the Abel-Poisson sums in the weighted Lebesgue spaces with variable exponent are obtained. In the classical Lebesgue spaces these estimations were proved by M. F. Timan. The considered weight functions satisfy the well known Muckenhout condition. For the proofs of main results some estimations obtained in the classical weighted Lebesgue spaces and also an extrapolation theorem proved in the weighted variable exponent Lebesgue spaces are used. Main results are new even in the nonweighted variable exponent Lebesgue spaces.

Keywords

Zygmund means, Fejér means, Abel-Poisson means, Muckenhoupt weights, variable exponent Lebesgue spaces

Supporting Institution

TUBITAK grant 114F422: Approximation Problems in the Variable Exponent Lebesgue Spaces

Project Number

114F422

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