On the dual of Besov-Lorentz spaces

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.