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Sharp Interpolation Theorems in Couples of $L_p$ Spaces for Generalized Lions–Peetre Spaces of Means

V. I. Ovchinnikov

Voronezh State University

Abstract: Sharp interpolation theorems for linear operators acting on arbitrary couples of $L_p$ spaces are found in the family of generalized Lions–Peetre spaces of means. This family includes the Lorentz spaces with functional quasi-concave parameters, the Orlicz spaces, and spaces similar to them.

Keywords: Lebesgue space, Lorentz space with functional parameters, Orlicz space, interpolation theorem for linear operators, sharp interpolation theorem, generalized Lions–Peetre space of means.

UDC: 517.982

Received: 31.01.2011

DOI: 10.4213/faa3090

 English version: Functional Analysis and Its Applications, 2012, 46:4, 313–315

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