- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 3
- Linear methods of approximation in weighted Lebesgue spaces with variable exponent
Linear methods of approximation in weighted Lebesgue spaces with variable exponent
Authors : Ahmet Testici, Daniyal M. Israfilzade
Pages : 744-753
Doi:10.15672/hujms.798028
View : 9 | Download : 4
Publication Date : 2021-06-07
Article Type : Research
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