On the dual of Besov-Lorentz spaces

We work with Besov spaces with Lorentz smoothness Bˢ q Lp,r (Rⁿ ) . Here -∞<s< ∞ and 0<p,q,r<∞ . We determine the dual of Bˢ q Lp,r (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 ∞ ,r . We apply the results to determine the dual of certain Triebel-Lizorkin-Lorentz spaces Fˢ q Lp,r (Rⁿ ) .