Martingale operators and Hardy spaces generated by them

Ferenc Weisz

Displaying similar documents to “Martingale operators and Hardy spaces generated by them”

Inequalities relative to two-parameter Vilenkin-Fourier coefficients

Ferenc Weisz (1991)

Studia Mathematica

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Conjugate martingale transforms

Ferenc Weisz (1992)

Studia Mathematica

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Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.

Schatten classes and commutators on simple martingales

J. Chao, Lizhong Peng (1996)

Colloquium Mathematicae

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$(H_{p}, L_{p})$ -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.

Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients

Péter Simon, Ferenc Weisz (1997)

Studia Mathematica

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Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) $(\sum_{k = 1}^{\infty} \sum_{j = 1}^{\infty} {| f ̂ (k, j) |}^{p} {(k j)}^{p - 2})^{1 / p} \leq C_{p} ∥ f ∥_{H_{* *}^{p}}$ (1/2 < p≤2) where f belongs to the Hardy space $H_{* *}^{p} (G_{m} \times G_{s})$ defined by means of a maximal function. This inequality is extended to p > 2 if the Vilenkin-Fourier coefficients of f form a monotone sequence. We show that the converse of (*) also holds for all p > 0 under the monotonicity assumption.

Abel means of operator-valued processes

G. Blower (1995)

Studia Mathematica

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Let $(X_{j})$ be a sequence of independent identically distributed random operators on a Banach space. We obtain necessary and sufficient conditions for the Abel means of $X_{n} . . . X_{2} X_{1}$ to belong to Hardy and Lipschitz spaces a.s. We also obtain necessary and sufficient conditions on the Fourier coefficients of random Taylor series with bounded martingale coefficients to belong to Lipschitz and Bergman spaces.

On compact Ito's formulas for martingales of m .

María Jolis (1990)

Publicacions Matemàtiques

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We prove that the class m of continuous martingales with parameter set [0,1], bounded in L, is included in the class of semi-martingales S (L(P)) defined by Allain in [A]. As a consequence we obtain a compact Itô's formula. Finally we relate this result with the compact Itô formula obtained by Sanz in [S] for martingales of m .

Again on the weak law in martingale type p Banach spaces.

D. Hun Hong, M. Ordóñez Cabrera, S. Hak Sung, A. I. Volodin (1999)

Extracta Mathematicae

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The local versions of $H^{p} (ℝ^{n})$ spaces at the origin

Shan Lu, Da Yang (1995)

Studia Mathematica

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Let 0 < p ≤ 1 < q < ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces $H K ̇_{q}^{α, p} (ℝ^{n})$ which are the local versions of $H^{p} (ℝ^{n})$ spaces at the origin. Characterizations of these spaces in terms of atomic and molecular decompositions are established, together with their φ-transform characterizations in M. Frazier and B. Jawerth’s sense. We also prove an interpolation theorem for operators on $H K ̇_{q}^{α, p} (ℝ^{n})$ and discuss the $H K ̇_{q}^{α, p} (ℝ^{n})$ -boundedness of Calderón-Zygmund operators. Similar results can also be obtained...

On the class LlogL, martingales, and singular integrals

Richard Gundy (1969)

Studia Mathematica

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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...