NDLI: Infinitesimal Carleson Property for Weighted Measures Induced by Analytic Self-Maps of the Unit Disk

Content Provider	Springer Nature Link
Author	Li, Daniel Queffélec, Hervé Rodríguez Piazza, Luis
Copyright Year	2012
Abstract	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.
Starting Page	1371
Ending Page	1387
Page Count	17
File Format	PDF
ISSN	16618254
Journal	Complex Analysis and Operator Theory
Volume Number	7
Issue Number	4
e-ISSN	16618262
Language	English
Publisher	Springer Basel
Publisher Date	2012-06-07
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Calderón–Zygmund decomposition Carleson measure Weighted Bergman space Bounded analytic functions Bergman spaces, Fock spaces Banach spaces of continuous, differentiable or analytic functions Composition operators Mathematics Operator Theory Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Theory and Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Composition Operators on Weighted Bergman–Orlicz Spaces on the Ball

Order Bounded Weighted Composition Operators Mapping into the Bergman Space

Toeplitz Operators with BMO Symbols on Holomorphic Besov Spaces

Carleson Conditions in Bergman–Orlicz Spaces

Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

Carleson Measures for Spaces of Dirichlet Type

On the Li-Stević Integral Type Operators from Weighted Bergman Spaces into β-Zygmund Spaces

Composition Followed by Differentiation Between H $^{∞}$ and Zygmund Spaces

On the Spectrum of Volterra-Type Integral Operators on Fock–Sobolev Spaces

Infinitesimal Carleson Property for Weighted Measures Induced by Analytic Self-Maps of the Unit Disk

Similar Documents

Composition Operators on Weighted Bergman–Orlicz Spaces on the Ball

Order Bounded Weighted Composition Operators Mapping into the Bergman Space

Toeplitz Operators with BMO Symbols on Holomorphic Besov Spaces

Carleson Conditions in Bergman–Orlicz Spaces

Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

Carleson Measures for Spaces of Dirichlet Type

On the Li-Stević Integral Type Operators from Weighted Bergman Spaces into β-Zygmund Spaces

Composition Followed by Differentiation Between H $^{∞}$ and Zygmund Spaces

On the Spectrum of Volterra-Type Integral Operators on Fock–Sobolev Spaces

Infinitesimal Carleson Property for Weighted Measures Induced by Analytic Self-Maps of the Unit Disk