共查询到20条相似文献,搜索用时 795 毫秒
1.
Boo Rim Choe 《Journal of Mathematical Analysis and Applications》2011,379(2):889-909
Recently Li et al. have characterized, except for a critical case, the weighted Bergman spaces over the complex ball by means of integrability conditions of double integrals associated with difference quotients of holomorphic functions. In this paper we extend those characterizations to the case of weighted harmonic Bergman spaces over the real ball and complement their results by providing a characterization for the missing critical case. We also investigate the possibility of extensions to the half-space setting. Our observations reveal an interesting half-space phenomenon caused by the unboundedness of the half-space. 相似文献
2.
Stevo Stevi? 《Applied mathematics and computation》2010,217(5):1811-6197
We find an asymptotically equivalent expression to the essential norm of differences of weighted composition operators between weighted-type spaces of holomorphic functions on the unit ball in CN. As a consequence we characterize the compactness of these operators. The boundedness of these operators is also characterized. 相似文献
3.
K. Avetisyan Y. Tonoyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2012,47(5):209-220
In this paper continuous embeddings in spaces of harmonic functions with mixed norm on the unit ball in ? n are established, generalizing some Hardy-Littlewood embeddings for similar spaces of holomorphic functions in the unit disc. Differences in indices between the spaces of harmonic and holomorphic spaces are revealed. As a consequence an analogue of classical Fejér-Riesz inequality is obtained. Embeddings in the special case of Riesz systems are also established. 相似文献
4.
In this paper, we study the composition operator CΦ with a smooth but not necessarily holomorphic symbol Φ. A necessary and sufficient condition on Φ for CΦ to be bounded on holomorphic (respectively harmonic) weighted Bergman spaces of the unit ball in Cn (respectively Rn) is given. The condition is a real version of Wogen's condition for the holomorphic spaces, and a non-vanishing boundary Jacobian condition for the harmonic spaces. We also show certain jump phenomena on the weights for the target spaces for both the holomorphic and harmonic spaces. 相似文献
5.
Wolfgang Lusky 《Mathematische Nachrichten》1992,159(1):279-289
Weighted spaces of harmonic and holomorphic functions on the unit disc are discussed. It is shown that these spaces are always subspaces of c0. Moreover, for many weights, it is shown that the weighted space of holomorphic functions has a basis. 相似文献
6.
RiemannStieltjes integrals are considered as linear operatorson weighted Bloch and Bergman spaces of the open unit ball inseveral complex variables. For weighted Bloch spaces, boundedness,compactness and weak compactness of RiemannStieltjesoperators are characterized by means of certain growth propertiesof holomorphic symbols. For weighted Bergman spaces, some criteriaare given for RiemannStieltjes operators with holomorphicsymbols to be bounded, compact and of Schattenvon Neumann'sideal. 相似文献
7.
We investigate weighted composition operators that attain their norm on weighted Banach spaces of holomorphic functions on the unit disc of type H ∞. Applications for composition operators on weighted Bloch spaces are given. 相似文献
8.
Renata Otá halová 《Proceedings of the American Mathematical Society》2008,136(7):2483-2492
For the standard weighted Bergman spaces on the complex unit ball, the Berezin transform of a bounded continuous function tends to this function pointwise as the weight parameter tends to infinity. We show that this remains valid also in the context of harmonic Bergman spaces on the real unit ball of any dimension. This generalizes the recent result of C. Liu for the unit disc, as well as the original assertion concerning the holomorphic case. Along the way, we also obtain a formula for the corresponding weighted harmonic Bergman kernels.
9.
On Weighted Spaces of Harmonic and Holomorphic Functions 总被引:8,自引:0,他引:8
Weighed spaces of harmonic and holomorphic functions on theunit disc are studied. We show that for all radial weights whichare not decreasing too fast the space of harmonic functionsis isomorphic to c0. For the weights that we consider we completelycharacterize those spaces of holomorphic functions which areisomorphic to c0. Moreover, we determine when the Riesz projection,mapping the weighted space of harmonic functions onto the correspondingspace of holomorphic functions, is bounded. 相似文献
10.
V. S. Guliyev Zhijian Wu 《分析论及其应用》2005,21(2):143-156
We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included. 相似文献
11.
1IntroductionAcomplexBanachspacewithvaluesinwhicheveryboundedallalyticfunctionontheopenunitdiskhasradialliniltsatalmostallboundarypointsissaidtohavetheanalyticRa.don-NikodympropertyApaPerofBukhvalovandDanilevich[5lexanlinesthistopic.TheclassofBanachspaceswiththeanalyticRadon-Niliodympropertyisslightlylargerthanthatwiththeffedon-NikodympropertyIndeed,itisshownill[5]thatL1andmoregenerallyallBanachlatticesnotcontainingcoalsoverifytheanalyticffedon-NikodympropertyAftertheirwork,severalchaJra… 相似文献
12.
该文将几个全纯函数空间的定义从单复变数推广到多复变数, 这些空间中全纯函数的增长性依赖于某个权函数. 作者研究了它们的增长性与边界值的关系以及这些空间相互之间的对偶关系, 所用方法和技巧与单复变数有不少区别. 所得到的结论是单复变数许多已知结果的推广. 相似文献
13.
We investigate the isometries between weighted spaces of harmonic functions. We show that, under some mild conditions, every
isometry is a composition operator. Our research shows that the structure of isometries of weighted spaces of harmonic functions
is, in general, simpler than that observed for weighted spaces of holomorphic functions.
Supported by MEC and FEDER Project MTM 2005-08210. 相似文献
14.
It is shown that membership of holomorphic functions in Hardy-Sobolev spaces in the unit ball cannot be characterized by finiteness of any integral norm. In addition, sufficient conditions are given for a holomorphic function to be a pointwise multiplier of a Hardy-Sobolev space.
15.
The boundedness and compactness of composition operators between Bloch type spaces and Zygmund spaces of holomorphic functions
in the unit ball are characterized in the paper. 相似文献
16.
Elke Wolf 《Journal of Mathematical Analysis and Applications》2007,329(1):530-546
We consider weighted Fréchet spaces of holomorphic functions which are defined as countable intersections of weighted Banach spaces of type H∞. We study when these spaces have Stefan Heinrich's density condition and when they are distinguished. 相似文献
17.
Miroslav Engliš 《复变函数与椭圆型方程》2015,60(12):1712-1726
We obtain a formula for the Sobolev inner product in standard weighted Bergman spaces of holomorphic functions on a bounded symmetric domain in terms of the Peter–Weyl components in the Hua–Schmidt decomposition, and use it to clarify the relationship between the analytic continuation of these standard weighted Bergman spaces and the Sobolev spaces on bounded symmetric domains. 相似文献
18.
and spaces consist of all those locally integrable functions
on the open unit ball such that their mean oscillations on any Bergman
ball are, respectively, bounded and vanishing to zero as the Bergman ball
approaches the boundary of the unit ball. The harmonic (or analytic) versions
of the and spaces are the Bloch space and the little Bloch
space, respectively. The study of these spaces plays an important role in modern
analysis, especially in the the area of operator theory and holomorphic
spaces. In this paper, we characterize systematically the multipliers of and spaces.
Submitted: January 9, 2001?Revised: October 16, 2002 相似文献
19.
《Indagationes Mathematicae (Proceedings)》1989,92(3):315-321
The author characterizes two Carleson-type measures relative to Hardy spaces of functions, holomorphic in the unit ball of CN. 相似文献
20.
We consider the question for what kind of square integrable holomorphic functions f,g on the unit ball the densely defined products TfTg-are invertible and Fredholm on the weighted Bergman space of the unit ball.We furthermore obtain necessary and sufficient conditions for bounded Haplitz products HfTg-,where f∈L2(Bn,dvα) and g is a square integrable holomorphic function. 相似文献