On Besov spaces of logarithmic smoothness and Lipschitz spaces

Cobos Díaz, Fernando; Domínguez Bonilla, Óscar

On Besov spaces of logarithmic smoothness and Lipschitz spaces

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Official URL

https//doi.org/10.1016/j.jmaa.2014.12.034

Publication date

2015

Authors

Cobos Díaz, Fernando

Domínguez Bonilla, Óscar

Publisher

Elsevier

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URI

https://hdl.handle.net/20.500.14352/22984

Abstract

We compare Besov spaces B-p,q(0,b) with zero classical smoothness and logarithmic smoothness b defined by using the Fourier transform with the corresponding spaces:B-p,q(0,b) defined by means of the modulus of smoothness. In particular, we show that B-p,q(0,b+1/2) = B-2,2(0,b) for b > -1/2. We also determine the dual of In:B-p,q(0,b) with the help of logarithmic Lipschitz spaces Lip(p,q)((1,-alpha)) Finally we show embeddings between spaces Lip(p,q)((1,-alpha)) and B-p,q(1,b) which complement and improve embeddings established by Haroske (2000).