Interpolation of Marcinkiewicz spaces.
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Michael Cwikel, Per Nilsson (1985)
Mathematica Scandinavica
Walter Bloom (1980)
Studia Mathematica
L.I. Nikolova, L.E. Persson (1993)
Mathematica Scandinavica
Peleshenko, B.I. (2008)
Sibirskij Matematicheskij Zhurnal
John Cerda, Joaquim Martin (1996)
Mathematica Scandinavica
Jesús Bastero, Francisco Ruiz (1993)
Studia Mathematica
Under some assumptions on the pair , we study equivalence between interpolation properties of linear operators and monotonicity conditions for a pair (Y,Z) of rearrangement invariant quasi-Banach spaces when the extreme spaces of the interpolation are . Weak and restricted weak intermediate spaces fall within our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.
D. Fernandez, J. Garcia (1991)
Studia Mathematica
Joan Cerdà, Joaquim Martín, Pilar Silvestre (2011)
Banach Center Publications
If C is a capacity on a measurable space, we prove that the restriction of the K-functional to quasicontinuous functions f ∈ QC is equivalent to . We apply this result to identify the interpolation space .
Mieczysław Mastyło, Mario Milman (1999)
Studia Mathematica
Certain operator ideals are used to study interpolation of operators between spaces generated by the real method. Using orbital equivalence a new reiteration formula is proved for certain real interpolation spaces generated by ordered pairs of Banach lattices of the form . As an application we extend Ovchinnikov’s interpolation theorem from the context of classical Lions-Peetre spaces to a larger class of real interpolation spaces. A description of certain abstract J-method spaces is also presented....
William Kraynek (1972)
Studia Mathematica
Pedro Fernández Martínez (2006)
Revista Matemática Complutense
We study the behavior of the ball measure of non-compactness under several interpolation methods. First we deal with methods that interpolate couples of spaces, and then we proceed to extend the results to methods that interpolate finite families of spaces. We will need an approximation hypothesis on the target family of spaces.
Fernando Cobos, Pedro Fernández-Martínez, Antón Martínez (1999)
Studia Mathematica
We investigate the behaviour of the measure of non-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.
B. Jawerth, M. Milman (1989)
Mathematische Zeitschrift
Michael Cwikel, Archil Gulisashvili (2000)
Studia Mathematica
We study a problem of interpolating a linear operator which is bounded on some family of characteristic functions. A new example is given of a Banach couple of function spaces for which such interpolation is possible. This couple is of the form where B is an arbitrary Banach lattice of measurable functions on a σ-finite nonatomic measure space (Ω,Σ,μ). We also give an equivalent expression for the norm of a function ⨍ in the real interpolation space in terms of the characteristic functions of...
Brandani da Silva, Eduardo, Fernandez, Dicesar L. (2001)
Lobachevskii Journal of Mathematics
Mieczysłav Mastyło (1986)
Commentationes Mathematicae Universitatis Carolinae
Luigi D'Onofrio, Tadeusz Iwaniec (2003)
Studia Mathematica
We establish an interpolation theorem for a class of nonlinear operators in the Lebesgue spaces arising naturally in the study of elliptic PDEs. The prototype of those PDEs is the second order p-harmonic equation . In this example the p-harmonic transform is essentially inverse to . To every vector field our operator assigns the gradient of the solution, . The core of the matter is that we go beyond the natural domain of definition of this operator. Because of nonlinearity our arguments...
Popa, Nicolae (1982)
Proceedings of the 10th Winter School on Abstract Analysis
Lars Erik Persson (1986)
Mathematica Scandinavica
Jürgen Auterhoff (1983)
Mathematische Zeitschrift