排序方式: 共有13条查询结果,搜索用时 31 毫秒
1.
Pascal Lefèvre Daniel Li Hervé Queffélec Luis Rodríguez-Piazza 《Mathematische Annalen》2011,351(2):305-326
We show that the maximal Nevanlinna counting function and the Carleson function of analytic self-maps of the unit disk are
equivalent, up to constants. 相似文献
2.
Infinitesimal Carleson Property for Weighted Measures Induced by Analytic Self-Maps of the Unit Disk
Daniel Li Hervé Queffélec Luis Rodríguez-Piazza 《Complex Analysis and Operator Theory》2013,7(4):1371-1387
We prove that, for every $\alpha > -1$ , the pull-back measure $\varphi ({\mathcal A }_\alpha )$ of the measure $d{\mathcal A }_\alpha (z) = (\alpha + 1) (1 - |z|^2)^\alpha \, d{\mathcal A } (z)$ , where ${\mathcal A }$ is the normalized area measure on the unit disk $\mathbb D $ , by every analytic self-map $\varphi :\mathbb D \rightarrow \mathbb D $ is not only an $(\alpha \,{+}\, 2)$ -Carleson measure, but that the measure of the Carleson windows of size $\varepsilon h$ is controlled by $\varepsilon ^{\alpha + 2}$ times the measure of the corresponding window of size $h$ . This means that the property of being an $(\alpha + 2)$ -Carleson measure is true at all infinitesimal scales. We give an application by characterizing the compactness of composition operators on weighted Bergman–Orlicz spaces. 相似文献
3.
We show that the existence of a martingale approximation of a stationary process depends on the choice of the filtration. There exists a stationary linear process which has a martingale approximation with respect to the natural filtration, but no approximation with respect to a larger filtration with respect to which it is adapted and regular. There exists a stationary process adapted, regular, and having a martingale approximation with respect to a given filtration but not (regular and having a martingale approximation) with respect to the natural filtration. 相似文献
4.
G. Lechner D. Li H. Queffélec L. Rodríguez-Piazza 《Journal of Functional Analysis》2018,274(7):1928-1958
We study the approximation numbers of weighted composition operators on the Hardy space on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators with specific weights, we show how much the weight w can improve the decay rate of the approximation numbers, and give sharp upper and lower bounds. These examples are motivated from applications to the analysis of relative commutants of special inclusions of von Neumann algebras appearing in quantum field theory (Borchers triples). 相似文献
5.
We randomly construct various subsets A of the integers which have both smallness and largeness properties. They are small
since they are very close, in various senses, to Sidon sets: the continuous functions with spectrum in Λ have uniformly convergent
series, and their Fourier coefficients are in ℓp for all p > 1; moreover, all the Lebesgue spaces L
Λ
q
are equal forq < +∞. On the other hand, they are large in the sense that they are dense in the Bohr group and that the space of the bounded
functions with spectrum in Λ is nonseparable. So these sets are very different from the thin sets of integers previously known. 相似文献
6.
Pascal Lefèvre Daniel Li Hervé Queffélec Luis Rodríguez-Piazza 《Israel Journal of Mathematics》2013,195(2):801-824
We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space H 2. The last ones are connected with Hardy-Orlicz and Bergman-Orlicz spaces ${H^\psi }$ and ${B^\psi }$ , and provide a negative answer to the question of knowing if all composition operators which are weakly compact on a non-reflexive space are norm-compact. 相似文献
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We consider here the algebra of functions which are analytic and bounded in the right half-plane and can moreover be expanded
as an ordinary Dirichlet series. We first give a new proof of a theorem of Bohr saying that this expansion converges uniformly
in each smaller half-plane; then, as a consequence of the alternative definition of this algebra as an algebra of functions
analytic in the infinite-dimensional polydisk, we first observe that it does not verify the corona theorem of Carleson; and
then, we give in a deterministic way a new quantitative proof of the Bohnenblust-Hille optimality theorem, through the construction
of a generalized Rudin-Shapiro sequence of polynomials. Finally, we compare this proof with probabilistic ones. 相似文献