The dual of weak $L^p$

Michael Cwikel

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Maximal seminorms on Weak $L^{1}$

Michael Cwikel, Charles Fefferman (1981)

Studia Mathematica

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Purely non-atomic weak $L^{p}$ spaces

Denny Leung (1997)

Studia Mathematica

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Let (Ω,∑,μ) be a purely non-atomic measure space, and let 1 < p < ∞. If $L^{p, \infty} (Ω, \sum, μ)$ is isomorphic, as a Banach space, to $L^{p, \infty} (Ω^{'}, \sum^{'}, μ^{'})$ for some purely atomic measure space (Ω’,∑’,μ’), then there is a measurable partition $Ω = Ω_{1} \cup Ω_{2}$ such that $(Ω_{1}, Σ \cap Ω_{1}, μ |_{Σ \cap Ω_{1}})$ is countably generated and σ-finite, and that μ(σ) = 0 or ∞ for every measurable $σ \subseteq Ω_{2}$ . In particular, $L^{p, \infty} (Ω, \sum, μ)$ is isomorphic to $ℓ^{p, \infty}$ .

The space Weak H¹

Robert Fefferman, Fernando Soria (1987)

Studia Mathematica

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Linear operations tensor products, and contractive projections in function spaces

M. Rao (1970)

Studia Mathematica

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The converse of the Hölder inequality and its generalizations

Janusz Matkowski (1994)

Studia Mathematica

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Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if $ʃ_{Ω} x y d μ \leq ϕ^{- 1} (ʃ_{Ω} ϕ \circ x d μ) ψ^{- 1} (ʃ_{Ω} ψ \circ x d μ)$ for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then...

The continuity of the rearrangement in $W^{1, p} (ℝ)$

J. M. Coron (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The level function in rearrangement invariant spaces.

Gord Sinnamon (2001)

Publicacions Matemàtiques

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An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.

Orlicz spaces based on families of measures

Robert Rosenberg (1970)

Studia Mathematica

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Isomorphism of certain weak $L^{p}$ spaces

Denny Leung (1993)

Studia Mathematica

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It is shown that the weak $L^{p}$ spaces $ℓ^{p, \infty}, L^{p, \infty} [0, 1]$ , and $L^{p, \infty} [0, \infty)$ are isomorphic as Banach spaces.

Intermediate spaces and interpolation, the complex method

A. Calderón (1964)

Studia Mathematica

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Displaying similar documents to “The dual of weak L p ”

Displaying similar documents to “The dual of weak $L^{p}$ ”