On Carleman's inequality

Alzer, Horst

Displaying similar documents to “On Carleman's inequality”

On the strong Cesàro summability of double orthogonal series

I. Szalay (1988)

Studia Mathematica

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On the (C,α≥0,β≥0)-summability of double orthogonal series

F. Móricz (1985)

Studia Mathematica

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On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Jun Tateoka (1994)

Studia Mathematica

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C. Watari [12] obtained a simple characterization of Lipschitz classes $L i p^{(p)} α (W) (1 \geq p \geq \infty, α > 0)$ on the dyadic group using the $L^{p}$ -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces $B_{p, q}^{α}$ on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces $B_{p, q}^{α}$ by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...

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...

Some theorems on orthogonal functions (1)

R. Paley (1931)

Studia Mathematica

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On the a.e. Divergence of the arithmetic means of double orthogonal series

F. Móricz, K. Tandori (1985)

Studia Mathematica

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On the existence of series solution of differential equations of generalized order

Al-Bassam, M.A. (1970)

Portugaliae mathematica

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The product of q-Bessel functions

Carlitz, L. (1962)

Portugaliae mathematica

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Origami

Παναγιώτης Τελώνης (1989-1990)

Ευκλείδης Α

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The value-distribution of lacunary series and a conjecture of Paley

Takafumi Murai (1981)

Annales de l'institut Fourier

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The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.