The functions that operate on of a discrete group
N.T. Varopoulos (1965)
Bulletin de la Société Mathématique de France
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N.T. Varopoulos (1965)
Bulletin de la Société Mathématique de France
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Schmidt, Klaus D., Waldschaks, Gerd (1991)
Portugaliae mathematica
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Rajendra Sinha (1976)
Studia Mathematica
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G. Gát (1998)
Studia Mathematica
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Let G be the Walsh group. For we prove the a. e. convergence σf → f(n → ∞), where is the nth (C,1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator We prove that σ* is of type (p,p) for all 1 < p ≤ ∞ and of weak type (1,1). Moreover, , where H is the Hardy space on the Walsh group.
S. Zaidman (1980)
Rendiconti del Seminario Matematico della Università di Padova
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Ferenc Móricz (1989)
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...
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]).
Haskell Rosenthal (1971)
Studia Mathematica
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