Vectorial Hankel operators, Carleson embeddings, and notions of BMOA
Rydhe, Eskil LU
(2017)
In Geometric and Functional Analysis
27(2).
p.427-451
- Abstract
Let (Formula presented.) denote the space of (Formula presented.)-valued analytic functions (Formula presented.) for which the Hankel operator (Formula presented.) is (Formula presented.)-bounded. Obtaining concrete characterizations of (Formula presented.) has proven to be notoriously hard. Let (Formula presented.) denote fractional differentiation. Motivated originally by control theory, we characterize (Formula presented.)-boundedness of (Formula presented.), where (Formula presented.), in terms of a natural anti-analytic Carleson embedding condition. We obtain three notable corollaries: The first is that (Formula presented.) is not characterized by said embedding condition. The second is that when we add an adjoint embedding... (More)
Let (Formula presented.) denote the space of (Formula presented.)-valued analytic functions (Formula presented.) for which the Hankel operator (Formula presented.) is (Formula presented.)-bounded. Obtaining concrete characterizations of (Formula presented.) has proven to be notoriously hard. Let (Formula presented.) denote fractional differentiation. Motivated originally by control theory, we characterize (Formula presented.)-boundedness of (Formula presented.), where (Formula presented.), in terms of a natural anti-analytic Carleson embedding condition. We obtain three notable corollaries: The first is that (Formula presented.) is not characterized by said embedding condition. The second is that when we add an adjoint embedding condition, we obtain a sufficient but not necessary condition for boundedness of (Formula presented.). The third is that there exists a bounded analytic function for which the associated anti-analytic Carleson embedding is unbounded. As a consequence, boundedness of an analytic Carleson embedding does not imply that the anti-analytic ditto is bounded. This answers a question by Nazarov, Pisier, Treil, and Volberg.
(Less)
- author
- Rydhe, Eskil
LU
- organization
- publishing date
- 2017-04
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Geometric and Functional Analysis
- volume
- 27
- issue
- 2
- pages
- 427 - 451
- publisher
- Birkhäuser
- external identifiers
-
- scopus:85014529498
- wos:000398727300005
- ISSN
- 1016-443X
- DOI
- 10.1007/s00039-017-0400-4
- language
- English
- LU publication?
- yes
- id
- d2012cd0-f443-4981-af5c-3b2570c282bf
- date added to LUP
- 2017-03-14 12:01:03
- date last changed
- 2025-01-07 09:33:31
@article{d2012cd0-f443-4981-af5c-3b2570c282bf,
abstract = {{<p>Let (Formula presented.) denote the space of (Formula presented.)-valued analytic functions (Formula presented.) for which the Hankel operator (Formula presented.) is (Formula presented.)-bounded. Obtaining concrete characterizations of (Formula presented.) has proven to be notoriously hard. Let (Formula presented.) denote fractional differentiation. Motivated originally by control theory, we characterize (Formula presented.)-boundedness of (Formula presented.), where (Formula presented.), in terms of a natural anti-analytic Carleson embedding condition. We obtain three notable corollaries: The first is that (Formula presented.) is not characterized by said embedding condition. The second is that when we add an adjoint embedding condition, we obtain a sufficient but not necessary condition for boundedness of (Formula presented.). The third is that there exists a bounded analytic function for which the associated anti-analytic Carleson embedding is unbounded. As a consequence, boundedness of an analytic Carleson embedding does not imply that the anti-analytic ditto is bounded. This answers a question by Nazarov, Pisier, Treil, and Volberg.</p>}},
author = {{Rydhe, Eskil}},
issn = {{1016-443X}},
language = {{eng}},
number = {{2}},
pages = {{427--451}},
publisher = {{Birkhäuser}},
series = {{Geometric and Functional Analysis}},
title = {{Vectorial Hankel operators, Carleson embeddings, and notions of BMOA}},
url = {{http://dx.doi.org/10.1007/s00039-017-0400-4}},
doi = {{10.1007/s00039-017-0400-4}},
volume = {{27}},
year = {{2017}},
}