Approximation problems in the Lebesgue spaces with variable exponent

DOI10.1016/j.jmaa.2017.10.067zbMath1395.46023OpenAlexW2766857724MaRDI QIDQ1684702

Daniyal M. Israfilov, Ahmet Testici

Publication date: 12 December 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.10.067

zbMATH Keywords

modulus of smoothnessdirect and inverse theoremsvariable exponent Lebesgue spacesapproximation by polynomialsgeneralized Lipschitz classes

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Approximation by polynomials (41A10)

Related Items (8)

Exponential approximation in variable exponent Lebesgue spaces on the real line ⋮ Unnamed Item ⋮ On the equivalence of the \(K\)-functional and the modulus of continuity on the periodic variable exponent Morrey spaces ⋮ Approximation in variable exponent spaces and growth of norms of trigonometric polynomials ⋮ Multiplier and approximation theorems in Smirnov classes with variable exponent ⋮ Unnamed Item ⋮ Direct and Inverse Theorems in Variable Exponent Smirnov Classes ⋮ Approximation by matrix transforms in generalized grand Lebesgue spaces with variable exponent

Cites Work

• Variable Lebesgue spaces. Foundations and harmonic analysis
• Lebesgue and Sobolev spaces with variable exponents
• Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent
• Some aspects of approximation theory in the spaces \(L^{p(x)}(E)\)
• Trigonometric approximation in generalized Lebesgue spaces L^p(x)
• Polynomial approximation of functions in weighted Lebesgue and Smirnov spaces with nonstandard growth
• Approximation in Smirnov classes with variable exponent
• Approximation of classes of functions defined by a generalized $r$-th modulus of smoothness
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• Approximation of functions in $ L^{p(x)}_{2\pi}$ by trigonometric polynomials
• A generalized modulus of smoothness
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