Boundedness of classical operators on classical Lorentz spaces

E. Sawyer

Displaying similar documents to “Boundedness of classical operators on classical Lorentz spaces”

A sharp rearrangement inequality for the fractional maximal operator

A. Cianchi, R. Kerman, B. Opic, L. Pick (2000)

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We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, $M_{γ} ⨍$ , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of $M_{γ}$ between classical Lorentz spaces.

Two weight function norm inequalities for the Hardy-Littlewood maximal function and the Hilbert transform

Benjamin Muckenhoupt, Richard Wheeden (1976)

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Two-weight norm inequalities for the Hardy-Little-wood maximal function for one-parameter rectangles

Oscar Salinas (1991)

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On reverse Hardy's inequality.

Alejandro García del Amo (1993)

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Best constants and asymptotics of Marcinkiewicz-Zygmund inequalities

Andreas Defant, Marius Junge (1997)

Studia Mathematica

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We determine the set of all triples 1 ≤ p,q,r ≤ ∞ for which the so-called Marcinkiewicz-Zygmund inequality is satisfied: There exists a constant c≥ 0 such that for each bounded linear operator $T : L_{q} (μ) \to L_{p} (ν)$ , each n ∈ ℕ and functions $f_{1}, . . ., f_{n} \in L_{q} (μ)$ , $(ʃ (\sum_{k = 1}^{n} | T f_{k} |^{r})^{p / r} {d ν)}^{1 / p} \leq c ∥ T ∥ (ʃ (\sum_{k = 1}^{n} | f_{k} |^{r} {)^{q / r} d μ)}^{1 / q}$ . This type of inequality includes as special cases well-known inequalities of Paley, Marcinkiewicz, Zygmund, Grothendieck, and Kwapień. If such a Marcinkiewicz-Zygmund inequality holds for a given triple (p,q,r), then we calculate the best constant c ≥ 0 (with the...

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...

Weighted Lorentz norm inequalities for integral operators

Elida Ferreyra (1990)

Studia Mathematica

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Denseness of the spaces $Φ_{V}$ of Lizorkin type in the mixed $L^{p ̅} (ℝ^{n})$ -spaces

Stefan Samko (1995)

Studia Mathematica

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Weighted norm inequalities for Riesz potentials and fractional maximal functions in mixed norm Lebesgue spaces

Tord Sjödin (1990)

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A characterization of probability measures by f-moments

K. Urbanik (1996)

Studia Mathematica

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Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments $ʃ_{0}^{\infty} ƒ (x) μ^{* n} (d x)$ (n = 1,2...). A function ƒ is said to have the identification propertyif probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function if it is infinitely differentiable on the open half-line (0,∞) and ${(- 1)}^{n} ƒ^{(n + 1)} (x)$ is completely monotone for some nonnegative integer n. The purpose...