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Approximation problems in the Lebesgue spaces with variable exponent. (English) Zbl 1395.46023

Authors’ abstract: In the variable exponent Lebesgue space, the \(r\)-th modulus of smoothness \((r=1,2,\ldots)\) is defined, and in this term, the direct and inverse theorems of approximation theory are proved. Moreover, the constructive characterization problems for some subclasses are discussed.

MSC:

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