Displaying similar documents to “Sharp summability for Monge transport density via interpolation”

Semivariation in L p -spaces

Brian Jefferies, Susumu Okada (2005)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that X and Y are Banach spaces and that the Banach space X ⊗ ^ τ Y is their complete tensor product with respect to some tensor product topology τ . A uniformly bounded X -valued function need not be integrable in X ⊗ ^ τ Y with respect to a Y -valued measure, unless, say, X and Y are Hilbert spaces and τ is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index 1 ≤ p < ∞ and suppose that X and Y are L p -spaces with τ p the associated...

The scalar Oseen operator - Δ + ∂ / ∂ x 1 in ℝ 2

Chérif Amrouche, Hamid Bouzit (2008)

Applications of Mathematics

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This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L p theory.

Stability for non-autonomous linear evolution equations with L p -maximal regularity

Hafida Laasri, Omar El-Mennaoui (2013)

Czechoslovak Mathematical Journal

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We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem ( P ) u ˙ ( t ) + A ( t ) u ( t ) = f ( t ) t -a.e. on [ 0 , τ ] , u ( 0 ) = 0 , where A : [ 0 , τ ] → ℒ ( X , D ) is a bounded and strongly measurable function and X , D are Banach spaces such that D → d ↪ X . Our main concern is to characterize L p -maximal regularity and to give an explicit approximation of the problem (P).