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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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 .
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...
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...
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...
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.
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...
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.
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)...
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...
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....
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...
Hun Hee Lee (2008)
Studia Mathematica
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We consider two operator space versions of type and cotype, namely -type, -cotype and type (p,H), cotype (q,H) for a homogeneous Hilbertian operator space H and 1 ≤ p ≤ 2 ≤ q ≤ ∞, generalizing “OH-cotype 2” of G. Pisier. We compute type and cotype of some Hilbertian operator spaces and spaces, and we investigate the relationship between a homogeneous Hilbertian space H and operator spaces with cotype (2,H). As applications we consider operator space versions of generalized little...
Rachid Boumahdi, Jesse Larone (2018)
Archivum Mathematicum
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Let be a polynomial with integral coefficients. Shapiro showed that if the values of at infinitely many blocks of consecutive integers are of the form , where is a polynomial with integral coefficients, then for some polynomial . In this paper, we show that if the values of at finitely many blocks of consecutive integers, each greater than a provided bound, are of the form where is an integer greater than 1, then for some polynomial .
José García-Cuerva
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CONTENTSIntroduction.......................................................................................................................................................... 5Chapter I. Some preliminary lemmas............................................................................................................ 8Chapter II. Weighted spaces of analytic functions.......................................................................... 13 1. Behaviour at the boundary..........................................................................................................................