What question did this study set out to answer?

This research aims to determine the dual of Besov spaces with Lorentz smoothness using wavelet characterization.

April 28, 2026Annali di Matematica Pura ed Applicata (1923 -)0 citationsOpen Access

On the dual of Besov-Lorentz spaces

FCFernando Cobos LFLuz M. Fernández-Cabrera TKThomas Kühn

Key Points

This research aims to determine the dual of Besov spaces with Lorentz smoothness using wavelet characterization.
Analyzed Besov spaces with Lorentz smoothness $$B^s_{q} L_{p,r}$$ for $$- iny ext{infty}<s< ext{infty}$$ and $$0<p,q,r< ext{infty}$$.
Applied characterization methods involving wavelets to establish dual spaces, particularly for $$p=1$$ and $$1<r< ext{infty}$$.
Investigated implications for determining the dual of Triebel-Lizorkin-Lorentz spaces $$F^s_{q} L_{p,r}$$.
Identified new Besov spaces as duals when $$p=1$$ and $$1<r< ext{infty}$$ using limiting Lorentz sequence spaces $$il_{ iny ext{infty},r}$$.
Established further connections between dual Besov spaces and Triebel-Lizorkin-Lorentz spaces.

Abstract

Abstract We work with Besov spaces with Lorentz smoothness Bˢ ₐ L₏, ₑ (Rⁿ). Here -<s< and 0<p, q, r<. We determine the dual of Bˢ ₐ L₏, ₑ (Rⁿ) with the help of its characterization in terms of wavelets. In particular, when p=1 and 1<r<, the dual spaces are new Besov spaces defined by using the limiting Lorentz sequence spaces, ₑ. We apply the results to determine the dual of certain Triebel-Lizorkin-Lorentz spaces Fˢ ₐ L₏, ₑ (Rⁿ).

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