Interpolation with a functional parameter in the class of Besov spaces (Q1357926)

Let \(A_p^s\) be the subspace in the Besov space \(B^s_p\), consisting of all analytic functions in the unit disk \(| z| <1\), where \(0<p\leq \infty\), \(-\infty<s<\infty\). The author characterizes the interpolation spaces, \((A^{s_0}_{p_0}, A^{s_1}_{p_1})_{f,q,K}\), with a quasi-norm, \(\| K(t,a,A^{s_0}_{p_0}, A^{s_1}_{p_1})/f(t)t^{1/q}\| _{L^q}\), \(0<q\leq \infty\), where \(K\) is the usual Peetre functional, and \(f\) is an appropriate continuous function. An application to the problem of rational approximation in the BMO-norm, or in the \(H_p\)-norm, is given.