THE Kt-FUNCTIONAL FOR THE INTERPOLATION COUPLE L∞(dμ L1(dv)), L∞(dv; L1(dμ))

Hess, Albrecht; Pisier, Gilles

doi:10.1093/qmath/46.3.333

Q J Math

1995

DOI: 10.1093/qmath/46.3.333

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THE K_t-FUNCTIONAL FOR THE INTERPOLATION COUPLE L^∞(dμ L¹(dv)), L^∞(dv; L¹(dμ))

Albrecht Hess¹,

Gilles Pisier²

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Cited by 5 publications

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Real interpolation and transposition of certain function spaces

Pisier

2011

Rev Mat Complut

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Our starting point is a lemma due to Varopoulos. We give a different proof of a generalized form this lemma, that yields an equivalent description of the K-functional for the interpolation couple (X 0 , X 1 ) where X 0 = L p0,∞ (µ 1 ; L q (µ 2 )) and X 1 = L p1,∞ (µ 2 ; L q (µ 1 )) where 0 < q < p 0 , p 1 ≤ ∞ and (Ω 1 , µ 1 ), (Ω 2 , µ 2 ) are arbitrary measure spaces. When q = 1, this implies that the space (X 0 , X 1 ) θ,∞ (0 < θ < 1) can be identified with a certain space of operators. We also give an extension of the Varopoulos Lemma to pairs (or finite families) of conditional expectations that seems of independent interest. The present paper is motivated by non-commutative applications that we choose to publish separately.Lemma 2. Consider f : Ω 1 ×Ω 2 → R measurable. Let X 1 = L ∞ (µ 1 ; L 1 (µ 2 )) and X 2 = L ∞ (µ 2 ; L 1 (µ 1 )). Consider the following two properties:

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Real interpolation and transposition of certain function spaces

Pisier

2011

Rev Mat Complut

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Exact minimizer for the couple (L∞,BV) and the one-dimensional analogue of the Rudin–Osher–Fatemi model

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2011

Journal of Approximation Theory

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2000

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THE K_t-FUNCTIONAL FOR THE INTERPOLATION COUPLE L^∞(dμ L¹(dv)), L^∞(dv; L¹(dμ))

Cited by 5 publications

References 2 publications

Real interpolation and transposition of certain function spaces

Real interpolation and transposition of certain function spaces

Exact minimizer for the couple (L∞,BV) and the one-dimensional analogue of the Rudin–Osher–Fatemi model

Nonstationary Panels, Cointegration in Panels and Dynamic Panels: A Survey

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