Interpolation theorem for Nikol’skii-Besov type spaceswith mixed metric

Abstract

In this paper we study the interpolation properties of Nikol’skii-Besov spaces with a dominant mixed derivative and mixed metric with respect to anisotropic and complex interpolation methods. An interpolation theorem is proved for a weighted discrete space of vector-valued sequences lαq (A). It is shown that the Nikol’skii-Besov space under study is a retract of the space lαq (Lp). Based on the above results, interpolation theorems were obtained for Nikol’skii-Besov spaces with the dominant mixed derivative and mixed metric.

Keywords

• Nikol’skii-Besov type spaces
• method of anisotropic interpolation
• complex interpolation