共查询到20条相似文献,搜索用时 0 毫秒
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A. Bonilla F. Pérez-González A. Stray R. Trujillo-González 《Journal d'Analyse Mathématique》1997,73(1):65-89
This paper is concerned with several approximation problems in the weighted Hardy spacesH
p(Ω) of analytic functions in the open unit disc D of the complex plane ℂ. We prove that ifX is a relatively closed subset of D, the class of uniform limits onX of functions inH
p(Ω) coincides, moduloH
p(Ω), with the space of uniformly continuous functions on a certain hull ofX which are holomorphic on its interior. We also solve the simultaneous approximation problems of describing Farrell and Mergelyan
sets forH
p(Ω), giving geometric characterizations for them. By replacing approximating polynomials by polynomial multipliers of outer
functions, our results lead to characterizations of the same sets with respect to cyclic vectors in the classical Hardy spacesH
p(D), 1 ⪯p < ∞.
Dedicated to Professor Nácere Hayek on the occasion of his 75th birthday. 相似文献
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Anisotropic weak Hardy spaces and interpolation theorems 总被引:1,自引:0,他引:1
In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces. 相似文献
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In this paper, we will characterize the weighted Hardy spaces by the intrinsic square functions including the Lusin area function, Littlewood-Paley G-function and -function. 相似文献
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In this paper, applying the atomic decomposition and molecular characterization of the real weighted Hardy spaces , we give the weighted boundedness of the homogeneous fractional integral operator from to , and from to . 相似文献
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In this paper we give sufficient conditions to imply
the $H^{1}_{w}-L^{1}_{w}$ boundedness of the Marcinkiewicz
integral operator $\mu_\Omega$, where w
is a Muckenhoupt weight. We also prove that, under the stronger condition
$\Omega \in {\rm Lip}_\alpha$, the operator $\mu_\Omega$ is bounded from
$H^{p}_{w}$ to $L^{p}_{w}$ for $\max\{n/(n+1/2), n/(n+\alpha)\}$ < p < 1. 相似文献
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It is known that the spline system of orderm is an unconditional basis forH p[0,1] whenp>1/(m+2) and a Schauder basis whenp ≧1/(m+2). We show that these results are sharp. 相似文献
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We proved the noncommutative analogue of Calderón’s result for fully symmetric spaces \(E_1\) and \(E_2\) on (0, 1) and for a finite von Neumann algebra \({{\mathcal {M}}}\). We also proved the noncommutative symmetric Hardy space’s analogue of Calderón’s result for fully symmetric spaces and for finite subdiagonal subalgebras. 相似文献
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In this paper we generalize an interpolation result due to J.-O. Strömberg and A. Torchinsky to the case of one-sided Hardy spaces. This generalization is important in the study of the weak type (1,1) for lateral strongly singular operators. We shall need an atomic decomposition in which for every atom there exists another atom supported contiguously at its right. In order to obtain this decomposition we have developed a rather simple technique to break up an atom into a sum of others atoms. 相似文献
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Several interpolation theorems on martingale Hardy spaces over weighted measure spaces are given. Our proofs are based on the atomic decomposition of martingale Hardy spaces over weighted measure spaces. As applications of interpolation theorems, some inequalities of martingale transform operator are obtained. 相似文献
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We continue studies begun by C.A. Micchelli and T.J. Rivlin on optimal recovery in Hp spaces. The feature operators are various interpolation operators drawn from the theory of Walsh equiconvergence, as are
the information sets. The theory is of interest in that it identifies linear algorithms which might not otherwise be isolated
for study or used as approximations of the feature operators. In some cases, we can identify the optimal algorithm although
we cannot explicitly determine the exact order of the approximation that it achieves.
For Charles Micchelli on his sixtieth birthday, with appreciation
Mathematics subject classifications (2000) 41A05, 30B30.
A. Sharma: Deceased. 相似文献
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H. M. Hayrapetyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(6):382-397
The paper considers the free interpolation problem in the Hardy weighted space H p(ρ). It is assumed that the weight ρ has unique singularity of the order αonly at the point 1. Particularly, for α − p[(α + 1)p −1] > 0 the corresponding free interpolation problem is stated and its solvability is proved. 相似文献
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加权Herz型Hardy空间上的Littlewood-Paley g函数 总被引:3,自引:0,他引:3
王月山 《纯粹数学与应用数学》2001,17(3):220-226
研究了Littlewood-Paley g函数gψ(f)(x)在加权Herz型Hardy空间上的性质,得到了如下结果,若ω1,ω2∈A1,则当n(1-1/q)≤α≤n(1-1/q) ε时,gψ为HK^a,p q(ω1,ω2)到K^a,p q(ω1,ω2)上的有界算子,当α=n(1-1/) ω时,gψ为HK^a,p q(ω1,ω2)到WK^a,p q(ω1,ω2)上的有界算子。 相似文献
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V. M. Dil’nyi 《Ukrainian Mathematical Journal》2008,60(9):1477-1482
We present an equivalent definition of functions analytic in the half-plane ℂ+ = {z: Re z > 0} for which
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1270–1274, September, 2008. 相似文献
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The molecular characterization of the weighted atomic Hardy space Hw p,q,s is given. As an application, the boundedness of Hilbert transform on the weighted Hardy space is proved. 相似文献
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We obtain estimates of the norm of Toeplitz operators on weighted Hardy and Besov spaces. As an application we give characterizations
of some spaces of pointwise multipliers. 相似文献
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This paper studies semigroups of operators on Hardy and Dirichlet spaces whose generators are differential operators of order greater than one. The theory of forms is used to provide conditions for the generation of semigroups by second order differential operators. Finally, a class of more general weighted Hardy spaces is considered and necessary and sufficient conditions are given for an operator of the form \(f \mapsto Gf^{(n_0)}\) (for holomorphic G and arbitrary \(n_0\)) to generate a semigroup of quasicontractions. 相似文献