Implementation of the Sparr Interpolation Method in Classes of Spaces of Smooth Functions

The multidimensional Sparr interpolation method is implemented in the Besov spaces $B^s_{p,q}$ and the Lizorkin–Triebel spaces $F^s_{p,q}$. It is shown that this results in Besov spaces of type $B^s_{p,q,(q)}$. An interpolation theorem for Besov spaces using weak conditions of the form $T\colon F^s_{p,1,(1)}\to F^{\widetilde s}_{\widetilde p,\infty,(\infty)}$ is formulated.