This article is cited in 3 papers

Interpolation of nonlinear operators in weighted $L_p$-spaces

V. M. Kaplitskiĭ

South Mathematical Institute of VSC RAS, Vladikavkaz

Abstract: We show that Peetre's classical interpolation theorem in weighted $L_p$-spaces is carried over to some classes of nonlinear operators containing in particular the Lipschitz operators and operators close to them in the properties satisfying less restrictive conditions than Lipschitz in each of the spaces of a Banach pair.

Keywords: nonlinear operator, $K$-functional, interpolation.

UDC: 517.988

Received: 11.12.2008

 English version: Siberian Mathematical Journal, 2010, 51:2, 255–266

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