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Interpolation methods of means and orbits

Mieczysław Mastyło (2005)

Studia Mathematica

Banach operator ideal properties of the inclusion maps between Banach sequence spaces are used to study interpolation of orbit spaces. Relationships between those spaces and the method-of-means spaces generated by couples of weighted Banach sequence spaces with the weights determined by concave functions and their Janson sequences are shown. As an application we obtain the description of interpolation orbits in couples of weighted L p -spaces when they are not described by the K-method. We also develop...

Interpolation of Banach spaces, differential geometry and differential equations.

Stephen Semmes (1988)

Revista Matemática Iberoamericana

In recent years the study of interpolation of Banach spaces has seen some unexpected interactions with other fields. (...) In this paper I shall discuss some more interactions of interpolation theory with the rest of mathematics, beginning with some joint work with Coifman [CS]. Our basic idea was to look for the methods of interpolation that had interesting PDE's arising as examples.

Interpolation of Cesàro sequence and function spaces

Sergey V. Astashkin, Lech Maligranda (2013)

Studia Mathematica

The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that C e s p ( I ) is an interpolation space between C e s p ₀ ( I ) and C e s p ₁ ( I ) for 1 < p₀ < p₁ ≤ ∞ and 1/p = (1 - θ)/p₀ + θ/p₁ with 0 < θ < 1, where I = [0,∞) or [0,1]. The same result is true for Cesàro sequence spaces. On the other hand, C e s p [ 0 , 1 ] is not an interpolation space between Ces₁[0,1] and C e s ∞ [ 0 , 1 ] .

Interpolation of operators when the extreme spaces are L ∞

Jesús Bastero, Francisco Ruiz (1993)

Studia Mathematica

Under some assumptions on the pair ( A 0 , B 0 ) , 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 L ∞ . Weak and restricted weak intermediate spaces fall within our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.

Currently displaying 241 – 260 of 438