Riesz-Zygmund means and approximation in variable exponent grand spaces. (English) Zbl 07887443
Summary: In the paper, the estimates of generalized modulus of smoothness and best approximation in variable exponent grand Lebesgue spaces in terms of norms of derivatives of Fourier partial sums, Riesz-Zygmund and Euler means are given. Some characterizations of generalized Hölder spaces are obtained in terms of Riesz-Zygmund means.
MSC:
| 42A10 | Trigonometric approximation |
| 41A17 | Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) |
| 41A50 | Best approximation, Chebyshev systems |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
Keywords:
variable exponent grand Lebesgue space; Riesz-Zygmund means; derivative; generalized modulus of smoothness; generalized Hölder spaceReferences:
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