اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدFinite unions of interpolating sequences for Hardy spaces
103
0
0.0
(
0
)
تأليف
Daniel H. Luecking
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A sequence which is a finite union of interpolating sequences for $H^infty$ have turned out to be especially important in the study of Bergman spaces. The Blaschke products $B(z)$ with such zero sequences have been shown to be exactly those such that the multiplication $f mapsto fB$ defines an operator with closed range on the Bergman space. Similarly, they are exactly those Blaschke products that boundedly divide functions in the Bergman space which vanish on their zero sequence. There are several characterizations of these sequences, and here we add two more to those already known. We also provide a particularly simple new proof of one of the known characterizations. One of the new characterizations is that they are interpolating sequences for a more general interpolation problem.
قيم البحث
اقرأ أيضاً
We set a framework for the study of Hardy spaces inherited by complements of analytic hypersurfaces in domains with a prior Hardy space structure. The inherited structure is a filtration, various aspects of which are studied in specific settings. For
punctured planar domains, we prove a generalization of a famous rigidity lemma of Kerzman and Stein. A stabilization phenomenon is observed for egg domains. Finally, using proper holomorphic maps, we derive a filtration of Hardy spaces for certain power-generalized Hartogs triangles, although these domains fall outside the scope of the original framework.
We extend the parameterization of sine-type functions in terms of conformal mappings onto slit domains given by Eremenko and Sodin to the more general case of generating functions of real complete interpolating sequences. It turns out that the cuts h
ave to fulfill the discrete Muckenhoupt condition studied earlier by Lyubarskii and Seip.
We study almost sure separating and interpolating properties of random sequences in the polydisc and the unit ball. In the unit ball, we obtain the 0-1 Komolgorov law for a sequence to be interpolating almost surely for all the Besov-Sobolev spaces $
B_{2}^{sigma}left(mathbb{B}_{d}right)$, in the range $0 < sigmaleq1 / 2$. For those spaces, such interpolating sequences coincide with interpolating sequences for their multiplier algebras, thanks to the Pick property. This is not the case for the Hardy space $mathrm{H}^2(mathbb{D}^d)$ and its multiplier algebra $mathrm{H}^infty(mathbb{D}^d)$: in the polydisc, we obtain a sufficient and a necessary condition for a sequence to be $mathrm{H}^infty(mathbb{D}^d)$-interpolating almost surely. Those two conditions do not coincide, due to the fact that the deterministic starting point is less descriptive of interpolating sequences than its counterpart for the unit ball. On the other hand, we give the $0-1$ law for random interpolating sequences for $mathrm{H}^2(mathbb{D}^d)$.
A description of the Bloch functions that can be approximated in the Bloch norm by functions in the Hardy space $H^p$ of the unit ball of $Cn$ for $0<p<infty$ is given. When $0<pleq1$, the result is new even in the case of the unit disk.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
