Hardy spaces on compact Lie groups
Brian E. Blank, Dashan Fan (1997)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Brian E. Blank, Dashan Fan (1997)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Jacek Dziubanski, Jacek Zienkiewicz (1999)
Revista Matemática Iberoamericana
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Let {T} be the semigroup of linear operators generated by a Schrödinger operator -A = Δ - V, where V is a nonnegative potential that belongs to a certain reverse Hölder class. We define a Hardy space H by means of a maximal function associated with the semigroup {T}. Atomic and Riesz transforms characterizations of H are shown.
Dashan Fan, Shanzhen Lu, Dachun Yang (1998)
Publicacions Matemàtiques
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In this paper, the authors introduce a kind of local Hardy spaces in R associated with the local Herz spaces. Then the authors investigate the regularity in these local Hardy spaces of some nonlinear quantities on superharmonic functions on R. The main results of the authors extend the corresponding results of Evans and Müller in a recent paper.
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.
Jacek Dziubański, Jacek Zienkiewicz (1997)
Studia Mathematica
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For a Schrödinger operator A = -Δ + V, where V is a nonnegative polynomial, we define a Hardy space associated with A. An atomic characterization of is shown.
Soulaymane Korry (2002)
Revista Matemática Complutense
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We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces F (R), for 0 < s < 1 and 1 < p, q < ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on F (R), for 0 < s < 1 and 1 < p, q < ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H (R).
Oscar Salinas (1991)
Studia Mathematica
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Yong Ding (1997)
Colloquium Mathematicae
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In this paper we introduce atomic Hardy spaces on the product domain and prove that rough singular integral operators with Hardy space function kernels are bounded on . This is an extension of some well known results.
Alejandro García del Amo (1993)
Collectanea Mathematica
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