On strengthening the Lebesgue Density Theorem
S. Taylor (1959)
Fundamenta Mathematicae
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S. Taylor (1959)
Fundamenta Mathematicae
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Dash, A.T. (1974)
Portugaliae mathematica
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A. Alexiewicz (1953)
Studia Mathematica
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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 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...
J. H. B. Kemperman (1964)
Compositio Mathematica
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T. Figiel, T. Iwaniec, A. Pełczyński (1984)
Studia Mathematica
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T. Świątkowski (1978)
Fundamenta Mathematicae
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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.
T. Zolezzi (1974)
Rendiconti del Seminario Matematico della Università di Padova
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Oscar Blasco (1991)
Publicacions Matemàtiques
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The duality between H1 and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained. In this paper we shall study such space in little more detail and we shall consider the H1-BMO duality for vector-valued functions in the more general setting of spaces of homogeneous type (see [CW]).