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Interpolation theorem for the p-harmonic transform

Luigi D'Onofrio, Tadeusz Iwaniec (2003)

Studia Mathematica

We establish an interpolation theorem for a class of nonlinear operators in the Lebesgue spaces s ( ) arising naturally in the study of elliptic PDEs. The prototype of those PDEs is the second order p-harmonic equation d i v | u | p - 2 u = d i v . In this example the p-harmonic transform is essentially inverse to d i v ( | | p - 2 ) . To every vector field q ( , ) our operator p assigns the gradient of the solution, p = u p ( , ) . The core of the matter is that we go beyond the natural domain of definition of this operator. Because of nonlinearity our arguments...

Interpolation theory and measures related to operator ideals

Cobos, Fernando (1999)

Nonlinear Analysis, Function Spaces and Applications

Given any operator ideal , there are two natural functionals γ ( T ) , β ( T ) that one can use to show the deviation of the operator T to the closed surjective hull of and to the closed injective hull of , respectively. We describe the behaviour under interpolation of γ and β . The results are part of joint works with A. Martínez, A. Manzano and P. Fernández-Martínez.

Intersection properties of balls in spaces of compact operators

Asvald Lima (1978)

Annales de l'institut Fourier

We study the connection between intersection properties of balls and the existence of large faces of the unit ball in Banach spaces. Hanner’s result that a real space has the 3.2 intersection property if an only if disjoint faces of the unit ball are contained in parallel hyperplanes is extended to infinite dimensional spaces. It is shown that the space of compact operators from a space X to a space Y has the 3.2 intersection property if and only if X and Y have the 3.2 intersection property and...

Intertwining Multiplication Operators on Function Spaces

Bahman Yousefi, Leila Bagheri (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Suppose that X is a Banach space of analytic functions on a plane domain Ω. We characterize the operators T that intertwine with the multiplication operators acting on X.

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