This article is cited in 3 papers

Research Papers

The quasinormed Neumann–Schatten ideals and embedding theorems for the generalized Lions–Peetre spaces of means

V. I. Ovchinnikov

Voronezh State University, Voronezh, Russia

Abstract: For the spaces $\varphi(X_0,X_1)_{p_0,p_1}$, which generalize the spaces of means introduced by Lions and Peetre to the case of functional parameters, necessary and sufficient conditions are found for embedding when all parameters (the function $\varphi$ and the numbers $1\leq p_0$, $p_1\leq\infty)$ vary. The proof involves a description of generalized Lions–Peetre spaces in terms of orbits and co-orbits of von Neumann–Schatten ideals (including quasinormed ideals).

Keywords: embedding theorems, method of means, functional parameter, generalized spaces.

Received: 20.05.2009

 English version: St. Petersburg Mathematical Journal, 2011, 22:4, 669–681

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