Interpolation of bilinear operators between Banach function spaces.
Interpolation of compact nonlinear operators.
Interpolation of compact operators by Goulaouic procedure
Interpolation of locally Hölder operators
Interpolation of Marcinkiewicz spaces.
Interpolation of multipliers of
Interpolation of nonlinear operators between families of Banach spaces.
Interpolation of operators of weak type .
Interpolation of Operators on Decreasing Functions.
Interpolation of operators when the extreme spaces are
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.
Interpolation of Orlicz-valued function spaces and U.M.D. property
Interpolation of quasicontinuous functions
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 .
Interpolation of real method spaces via some ideals of operators
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....
Interpolation of sublinear operators on generalized Orlicz and Hardy-Orlicz spaces
Interpolation of the measure of non-compactness between quasi-Banach spaces.
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.
Interpolation of the measure of non-compactness by the real method
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.
Interpolation of Weak Type Spaces.
Interpolation on families of characteristic functions
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...
Interpolation spaces with function parameter and measures of non-compactness.
Interpolation spaces