Interpolation of spaces of smooth functions. Chebyshev rational approximation on the circle (Q2761457)

In his previous papers the author describes real interpolation spaces of the couple of Besov spaces \((B^{s_0}_{p_0}, B_{p_1}^{s_1})\) with \(0< p_i <\infty\), \(s_0\neq s_1\), \(p_0\neq p_1\). To present the result he introduced a four parametric family of spaces \(BL^{sk}_{pq} (=(B^{s_0}_{p_0}, B_{p_1}^{s_1}) _{\theta q})\). The same results were obtained in this situation for Lizorkin-Triebel spaces. In the present paper these results are extended to the case \(p_0= \infty\).