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Interpolation d'opérateurs entre espaces de fonctions holomorphes

Patrice Lassere (1991)

Annales Polonici Mathematici

Let K be a compact subset of an hyperconvex open set D ⊂ ℂ n , forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to H ( D α ) is a continuous...

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.

Interpolation of quasicontinuous functions

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 K ( t , f ; L p ( C ) , L ∞ ( C ) ) to quasicontinuous functions f ∈ QC is equivalent to K ( t , f ; L p ( C ) ∩ Q C , L ∞ ( C ) ∩ Q C ) . We apply this result to identify the interpolation space ( L p ₀ , q ₀ ( C ) ∩ Q C , L p ₁ , q ₁ ( C ) ∩ Q C ) θ , q .

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