Jackson type inequalities for differentiable functions in weighted Orlicz spaces

Akgün, R.

doi:10.1090/spmj/1743

Jackson type inequalities for differentiable functions in weighted Orlicz spaces
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by R. Akgün

St. Petersburg Math. J. 34 (2023), 1-24

DOI: https://doi.org/10.1090/spmj/1743

Published electronically: December 16, 2022

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Abstract:

In the present work some Jackson Stechkin type direct theorems of trigonometric approximation are proved in Orlicz spaces with weights satisfying some Muckenhoupt $A_p$ condition. To obtain a refined version of the Jackson type inequality, an extrapolation theorem, Marcinkiewicz multiplier theorem, and Littlewood–Paley type results are proved. As a consequence, refined inverse Marchaud type inequalities are obtained. By means of a realization result, an equivalence is found between the fractional order weighted modulus of smoothness and Peetre’s classical weighted $K$-functional.

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