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Limiting reiteration for real interpolation with slowly varying functions
We present reiteration formulae with limiting values θ = 0 and θ = 1 for a real interpolation method involving slowly varying functions. Applications to the Lorentz–Karamata spaces, the FourierExpand
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Radial Fourier multipliers of L(R).
We give sufficient conditions (in terms of differentiability and growth properties) for a radial function to be an L(p)(R(2)) Fourier multiplier. These conditions are in the nature of best possible.
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Inequalities for moduli of smoothness versus embeddings of function spaces
The so-called sharp Marchaud inequality and some converse of it, as well as the Ulyanov and Kolyada inequalities are equivalent to some embeddings between Besov and potential spaces. Peetre’sExpand
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On weighted transplantation and multipliers for Laguerre expansions
Using the standard square--function method (based on the Poisson semigroup), multiplier conditions of H\"ormander type are derived for Laguerre expansions in $L^p$--spaces with power weights in theExpand
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Multipliers for (C,α)-bounded Fourier expansions in Banach spaces and approximation theory
General theory.- Multiplier criteria for (C,?)-bounded expansions.- Particular summation methods.- Applications to particular expansions.
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Fractional integration for Laguerre expansions
The aim of this note is to provide a fractional integration theorem in the framework of Laguerre expansions. The method of proof consists of establishing an asymptotic estimate for the involvedExpand
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Low regularity classes and entropy numbers
Abstract.We note a sharp embedding of the Besov space $$B^{\infty}_{0,q}({\mathbb{T}})$$ into exponential classes and prove entropy estimates for the compact embedding of subclasses with logarithmicExpand
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Embeddings for spaces of Lorentz–Sobolev type
The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel–Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. WeExpand
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