The converse of the Hölder inequality and its generalizations

Janusz Matkowski

Displaying similar documents to “The converse of the Hölder inequality and its generalizations”

$(H_{p}, L_{p})$ -type inequalities for the two-dimensional dyadic derivative

Ferenc Weisz (1996)

Studia Mathematica

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It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space $H_{p, q}$ to $L_{p, q}$ (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type $(L_{1}, L_{1})$ . As a consequence we show that the dyadic integral of a ∞ function $f \in L_{1}$ is dyadically differentiable and its derivative is f a.e.

$L^{p}$ -behaviour of the integral means of analytic functions

M. Mateljević, M. Pavlović (1984)

Studia Mathematica

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On a generalized Carleson inequality

D. Deng (1984)

Studia Mathematica

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On (C,1) summability of integrable functions with respect to the Walsh-Kaczmarz system

G. Gát (1998)

Studia Mathematica

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Let G be the Walsh group. For $f \in L^{1} (G)$ we prove the a. e. convergence σf → f(n → ∞), where $σ_{n}$ is the nth (C,1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator $σ * f ≔ s u p_{n} | σ_{n} f | .$ We prove that σ* is of type (p,p) for all 1 < p ≤ ∞ and of weak type (1,1). Moreover, $∥ σ * f ∥_{1} \leq c ∥ | f | ∥_{H}$ , where H is the Hardy space on the Walsh group.

Computing norms and critical exponents of some operators in $L^{p}$ -spaces

T. Figiel, T. Iwaniec, A. Pełczyński (1984)

Studia Mathematica

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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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Two-parameter Hardy-Littlewood inequality and its variants

Chang-Pao Chen, Dah-Chin Luor (2000)

Studia Mathematica

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Let s* denote the maximal function associated with the rectangular partial sums $s_{m n} (x, y)$ of a given double function series with coefficients $c_{j k}$ . The following generalized Hardy-Littlewood inequality is investigated: ${| | s * | |}_{p, μ} \leq C_{p, α, β} {Σ_{j = 0}^{\infty} Σ_{k = 0}^{\infty} {(j ̅)}^{p - α - 2} {(k ̅)}^{p - β - 2} {| c_{j k} |}^{p}}^{1 / p}$ , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on $c_{j k}$ and μ under which the above Hardy-Littlewood inequality holds. Several variants of this inequality are also examined. As a consequence, the ||·||p,μ-convergence property...

On reverse Hardy's inequality.

Alejandro García del Amo (1993)

Collectanea Mathematica

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Some remarks on Triebel spaces

Jürgen Marschall (1987)

Studia Mathematica

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Vector valued measures of bounded mean oscillation.

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]).

Characterization of $H^{p} (R^{n})$ in terms of generalized Littlewood-Paley g-functions

Akihito Uchiyama (1985)

Studia Mathematica

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