Linear methods of approximation in weighted Lebesgue spaces with variable exponent

Authors : Ahmet TESTİCİ, Daniyal M İSRAFİLZADE

Pages : 744-753

Doi:10.15672/hujms.798028

View : 27 | Download : 8

Publication Date : 2021-06-07

Article Type : Research Paper

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