On the dual of Besov-Lorentz spaces

Abstract We work with Besov spaces with Lorentz smoothness $$B^s _{q} L_{p,r} (\mathbb {R}^n )$$ . Here $$-\infty<s< \infty $$ and $$0<p,q,r<\infty $$ . We determine the dual of $$B^s _{q} L_{p,r} (\mathbb {R}^n )$$ with the help of its characterization in terms of wavelets. In particular, when $$p=1$$ and $$1<r<\infty $$ , the dual spaces are new Besov spaces defined by using the limiting Lorentz sequence spaces $$\ell _{\infty ,r}$$ . We apply the results to determine the dual of certain Triebel-Lizorkin-Lorentz spaces $$F^s _{q} L_{p,r} (\mathbb {R}^n )$$ .