Inequalities relative to two-parameter Vilenkin-Fourier coefficients
Ferenc Weisz (1991)
Studia Mathematica
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Ferenc Weisz (1991)
Studia Mathematica
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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.
J. Chao, Lizhong Peng (1996)
Colloquium Mathematicae
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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 to (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type . As a consequence we show that the dyadic integral of a ∞ function is dyadically differentiable and its derivative is f a.e.
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 (*) (1/2 < p≤2) where f belongs to the Hardy space 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.
G. Blower (1995)
Studia Mathematica
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Let be a sequence of independent identically distributed random operators on a Banach space. We obtain necessary and sufficient conditions for the Abel means of 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.
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 .
D. Hun Hong, M. Ordóñez Cabrera, S. Hak Sung, A. I. Volodin (1999)
Extracta Mathematicae
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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 which are the local versions of 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 and discuss the -boundedness of Calderón-Zygmund operators. Similar results can also be obtained...
Richard Gundy (1969)
Studia Mathematica
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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 of a given double function series with coefficients . The following generalized Hardy-Littlewood inequality is investigated: , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on 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...