This article is cited in 2 papers

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

V. L. Kreptogorskii

Kazan Branch Military Artillery University

Abstract: 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.

UDC: 517.982

Received: 27.01.2000

DOI: 10.4213/mzm770

 English version: Mathematical Notes, 2001, 70:4, 526–534

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