Vectorial Hankel operators, Carleson embeddings, and notions of BMOA
(2017) In Geometric and Functional Analysis 27(2). p.427451 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 antianalytic 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 antianalytic 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 antianalytic Carleson embedding is unbounded. As a consequence, boundedness of an analytic Carleson embedding does not imply that the antianalytic ditto is bounded. This answers a question by Nazarov, Pisier, Treil, and Volberg.
(Less)
 author
 Rydhe, Eskil ^{LU}
 organization
 publishing date
 201704
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Geometric and Functional Analysis
 volume
 27
 issue
 2
 pages
 427  451
 publisher
 Birkhauser Verlag Basel
 external identifiers

 scopus:85014529498
 wos:000398727300005
 ISSN
 1016443X
 DOI
 10.1007/s0003901704004
 language
 English
 LU publication?
 yes
 id
 d2012cd0f4434981af5c3b2570c282bf
 date added to LUP
 20170314 12:01:03
 date last changed
 20180107 11:55:14
@article{d2012cd0f4434981af5c3b2570c282bf, 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 antianalytic 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 antianalytic Carleson embedding is unbounded. As a consequence, boundedness of an analytic Carleson embedding does not imply that the antianalytic ditto is bounded. This answers a question by Nazarov, Pisier, Treil, and Volberg.</p>}, author = {Rydhe, Eskil}, issn = {1016443X}, language = {eng}, number = {2}, pages = {427451}, publisher = {Birkhauser Verlag Basel}, series = {Geometric and Functional Analysis}, title = {Vectorial Hankel operators, Carleson embeddings, and notions of BMOA}, url = {http://dx.doi.org/10.1007/s0003901704004}, volume = {27}, year = {2017}, }