Two more counterexamples to the infinite dimensional carleson embedding theorem
Rydhe, Eskil LU
(2018)
In International Mathematics Research Notices
2018(24).
p.7655-7680
- Abstract
The existence of a counterexample to the infinite-dimensional Carleson embedding theorem has been established by Nazarov, Pisier, Treil, and Volberg. We provide an explicit construction of such an example. We also obtain a non-constructive example of particularly simple form; the density function of the measure (with respect to a certain weighted area measure) is the tensor-square of a Hilbert space-valued analytic function. This special structure of the measure has implications for Hankel-like operators appearing in control theory.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/06007637-64bd-4e7b-b003-accf0806cd46
- author
- Rydhe, Eskil
LU
- organization
- publishing date
- 2018
- type
- Contribution to journal
- publication status
- published
- subject
- in
- International Mathematics Research Notices
- volume
- 2018
- issue
- 24
- pages
- 26 pages
- publisher
- Oxford University Press
- external identifiers
-
- scopus:85062018052
- ISSN
- 1073-7928
- DOI
- 10.1093/imrn/rnx120
- language
- English
- LU publication?
- yes
- id
- 06007637-64bd-4e7b-b003-accf0806cd46
- date added to LUP
- 2019-03-08 12:29:47
- date last changed
- 2025-10-14 09:22:55
@article{06007637-64bd-4e7b-b003-accf0806cd46,
abstract = {{<p>The existence of a counterexample to the infinite-dimensional Carleson embedding theorem has been established by Nazarov, Pisier, Treil, and Volberg. We provide an explicit construction of such an example. We also obtain a non-constructive example of particularly simple form; the density function of the measure (with respect to a certain weighted area measure) is the tensor-square of a Hilbert space-valued analytic function. This special structure of the measure has implications for Hankel-like operators appearing in control theory.</p>}},
author = {{Rydhe, Eskil}},
issn = {{1073-7928}},
language = {{eng}},
number = {{24}},
pages = {{7655--7680}},
publisher = {{Oxford University Press}},
series = {{International Mathematics Research Notices}},
title = {{Two more counterexamples to the infinite dimensional carleson embedding theorem}},
url = {{http://dx.doi.org/10.1093/imrn/rnx120}},
doi = {{10.1093/imrn/rnx120}},
volume = {{2018}},
year = {{2018}},
}