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Zbl 1206.42002
Akgün, Ramazan; Kokilashvili, Vakhtang
On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces. (English)
[J] Banach J. Math. Anal. 5, No. 1, 70-82, electronic only (2011). ISSN 1735-8787/e

The authors prove improved converse theorems of trigonometric approximation in variable exponent Lebesgue spaces with some Muckenhoupt weights, and as a corollary, they give improvements of the Marchaud inequality.
[Mehdi Hassani (Zanjan)]
MSC 2000:
*42A10 Trigonometric approximation
26A33 Fractional derivatives and integrals (real functions)
41A17 Inequalities in approximation
41A20 Approximation by rational functions

Keywords: weighted fractional moduli of smoothness; converse theorem; fractional derivative

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