On the Fejér-F. Riesz inequality in
Yoram Sagher (1977)
Studia Mathematica
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Yoram Sagher (1977)
Studia Mathematica
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Nobuhiro Asai (2007)
Colloquium Mathematicae
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The main aim of this short paper is to study Riesz potentials on one-mode interacting Fock spaces equipped with deformed annihilation, creation, and neutral operators with constants and , as in equations (1.4)-(1.6). First, to emphasize the importance of these constants, we summarize our previous results on the Hilbert space of analytic L² functions with respect to a probability measure on ℂ. Then we consider the Riesz kernels of order 2α, , on ℂ if , which can be derived from...
Nikolaos Atreas, Antonis Bisbas (2012)
Colloquium Mathematicae
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Let be a finite set of step functions or real valued trigonometric polynomials on = [0,1) satisfying a certain orthonormality condition. We study multiscale generalized Riesz product measures μ defined as weak-* limits of elements , where are -dimensional subspaces of L₂() spanned by an orthonormal set which is produced from dilations and multiplications of elements of and . The results involve mutual absolute continuity or singularity of such Riesz products extending previous...
Mouhamadou Dosso, Ibrahim Fofana, Moumine Sanogo (2013)
Annales Polonici Mathematici
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For 1 ≤ q ≤ α ≤ p ≤ ∞, is a complex Banach space which is continuously included in the Wiener amalgam space and contains the Lebesgue space . We study the closure in of the space of test functions (infinitely differentiable and with compact support in ) and obtain norm inequalities for Riesz potential operators and Riesz transforms in these spaces. We also introduce the Sobolev type space (a subspace of a Morrey-Sobolev space, but a superspace of the classical Sobolev space...
Adam Osękowski (2014)
Studia Mathematica
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We establish the following sharp local estimate for the family of Riesz transforms on . For any Borel subset A of and any function , , 1 < p < ∞. Here q = p/(p-1) is the harmonic conjugate to p, , 1 < p < 2, and , 2 ≤ p < ∞. This enables us to determine the precise values of the weak-type constants for Riesz transforms for 1 < p < ∞. The proof rests on appropriate martingale inequalities, which are of independent interest.
Bahri Turan (2006)
Studia Mathematica
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Let E be a Riesz space. By defining the spaces and of E, we prove that the center of is and show that the injectivity of the Arens homomorphism m: Z(E)” → Z(E˜) is equivalent to the equality . Finally, we also give some representation of an order continuous Banach lattice E with a weak unit and of the order dual E˜ of E in which are different from the representations appearing in the literature.
Albert Mas, Xavier Tolsa (2014)
Journal of the European Mathematical Society
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For integers and , we prove that an -dimensional Ahlfors-David regular measure in is uniformly -rectifiable if and only if the -variation for the Riesz transform with respect to is a bounded operator in . This result can be considered as a partial solution to a well known open problem posed by G. David and S. Semmes which relates the boundedness of the Riesz transform to the uniform rectifiability of .
Daniele Debertol (2006)
Studia Mathematica
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We consider the multiplier defined for ξ ∈ ℝ by , D denoting the open unit disk in ℝ. Given p ∈ ]1,∞[, we show that the optimal range of μ’s for which is a Fourier multiplier on is the same as for Bochner-Riesz means. The key ingredient is a lemma about some modifications of Bochner-Riesz means inside convex regions with smooth boundary and non-vanishing curvature, providing a more flexible version of a result by Iosevich et al. [Publ. Mat. 46 (2002)]. As an application, we show...
Simon Lücking (2014)
Studia Mathematica
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Let G be an infinite, compact abelian group and let Λ be a subset of its dual group Γ. We study the question which spaces of the form or and which quotients of the form or have the Daugavet property. We show that is a rich subspace of C(G) if and only if is a semi-Riesz set. If is a rich subspace of L¹(G), then is a rich subspace of C(G) as well. Concerning quotients, we prove that has the Daugavet property if Λ is a Rosenthal set, and that is a poor subspace of L¹(G)...
Xuefang Yan (2015)
Czechoslovak Mathematical Journal
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Let be a metric measure space endowed with a distance and a nonnegative Borel doubling measure . Let be a non-negative self-adjoint operator of order on . Assume that the semigroup generated by satisfies the Davies-Gaffney estimate of order and satisfies the Plancherel type estimate. Let be the Hardy space associated with We show the boundedness of Stein’s square function arising from Bochner-Riesz means associated to from Hardy spaces to , and also study...
David Swanson (2010)
Colloquium Mathematicae
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Let 1 ≤ p < ∞, k ≥ 1, and let Ω ⊂ ℝⁿ be an arbitrary open set. We prove a converse of the Calderón-Zygmund theorem that a function possesses an derivative of order k at almost every point x ∈ Ω and obtain a characterization of the space . Our method is based on distributional arguments and a pointwise inequality due to Bojarski and Hajłasz.
Edvard Kramar (2016)
Commentationes Mathematicae Universitatis Carolinae
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Denote by the commutator of two bounded operators and acting on a locally convex topological vector space. If , we show that is a quasinilpotent operator and we prove that if is a compact operator, then is a Riesz operator.
Elmiloud Chil, Mohamed Mokaddem, Bourokba Hassen (2015)
Commentationes Mathematicae Universitatis Carolinae
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Let be a Riesz space, a Hausdorff topological vector space (t.v.s.). We prove, under a certain separation condition, that any orthosymmetric bilinear map is automatically symmetric. This generalizes in certain way an earlier result by F. Ben Amor [On orthosymmetric bilinear maps, Positivity 14 (2010), 123–134]. As an application, we show that under a certain separation condition, any orthogonally additive homogeneous polynomial is linearly represented. This fits in the type of...
Richard Lechner
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We prove an interpolatory estimate linking the directional Haar projection to the Riesz transform in the context of Bochner-Lebesgue spaces , 1 < p < ∞, provided X is a UMD-space. If , the result is the inequality , (1) where the constant C depends only on n, p, the UMD-constant of X and the Rademacher type of . In order to obtain the interpolatory result (1) we analyze stripe operators , λ ≥ 0, which are used as basic building blocks to dominate the directional Haar projection....
Yu Liu, Jing Zhang, Jie-Lai Sheng, Li-Juan Wang (2016)
Czechoslovak Mathematical Journal
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Let be a Schrödinger operator and let be a Schrödinger type operator on , where is a nonnegative potential belonging to certain reverse Hölder class for . The Hardy type space is defined in terms of the maximal function with respect to the semigroup and it is identical to the Hardy space established by Dziubański and Zienkiewicz. In this article, we prove the -boundedness of the commutator generated by the Riesz transform , where , which is larger...
Steve Hofmann, Svitlana Mayboroda, Alan McIntosh (2011)
Annales scientifiques de l'École Normale Supérieure
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Let be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with , such as the heat semigroup and Riesz transform, are not, in general, of Calderón-Zygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in , Sobolev, and some new Hardy spaces naturally associated to . First, we show...
Anthony W. Hager (2016)
Commentationes Mathematicae Universitatis Carolinae
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The -property of a Riesz space (real vector lattice) is: For each sequence of positive elements of , there is a sequence of positive reals, and , with for each . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “” obtains for a Riesz space of continuous real-valued functions . A basic result is: For discrete , has iff the cardinal , Rothberger’s bounding number. Consequences...
B. Bojarski (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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For a function the notion of p-mean variation of order 1, is defined. It generalizes the concept of F. Riesz variation of functions on the real line ℝ¹ to ℝⁿ, n > 1. The characterisation of the Sobolev space in terms of is directly related to the characterisation of by Lipschitz type pointwise inequalities of Bojarski, Hajłasz and Strzelecki and to the Bourgain-Brezis-Mironescu approach.