On the Characterization of Triebel–Lizorkin Type Spaces of Analytic Functions
(2018) In Journal of Fourier Analysis and Applications 24(6). p.1491-1517- Abstract
We consider different characterizations of Triebel–Lizorkin type spaces of analytic functions on the unit disc. Even though our results appear in the folklore, detailed descriptions are hard to find, and in fact we are unable to discuss the full range of parameters. Without additional effort we work with vector-valued analytic functions, and also consider a generalized scale of function spaces, including for example so-called Q-spaces. The primary aim of this note is to generalize, and clarify, a remarkable result by Cohn and Verbitsky, on factorization of Triebel–Lizorkin spaces. Their result remains valid for functions taking values in an arbitrary Banach space, provided that the vector-valuedness “sits in the right factor”. On the... (More)
We consider different characterizations of Triebel–Lizorkin type spaces of analytic functions on the unit disc. Even though our results appear in the folklore, detailed descriptions are hard to find, and in fact we are unable to discuss the full range of parameters. Without additional effort we work with vector-valued analytic functions, and also consider a generalized scale of function spaces, including for example so-called Q-spaces. The primary aim of this note is to generalize, and clarify, a remarkable result by Cohn and Verbitsky, on factorization of Triebel–Lizorkin spaces. Their result remains valid for functions taking values in an arbitrary Banach space, provided that the vector-valuedness “sits in the right factor”. On the other hand, if we impose vector-valuedness on the “wrong” factor, then the factorization theorem fails even for functions taking values in a separable Hilbert space.
(Less)
- author
- Rydhe, Eskil LU
- organization
- publishing date
- 2018-12
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Factorization, Q-spaces, Triebel–Lizorkin spaces, Vector-valued analytic functions
- in
- Journal of Fourier Analysis and Applications
- volume
- 24
- issue
- 6
- pages
- 1491 - 1517
- publisher
- Springer
- external identifiers
-
- scopus:85036498420
- ISSN
- 1069-5869
- DOI
- 10.1007/s00041-017-9584-0
- language
- English
- LU publication?
- yes
- id
- bd3a4680-7263-4b01-b17b-033df6a7b7d9
- date added to LUP
- 2017-12-18 08:42:14
- date last changed
- 2024-06-24 08:25:44
@article{bd3a4680-7263-4b01-b17b-033df6a7b7d9, abstract = {{<p>We consider different characterizations of Triebel–Lizorkin type spaces of analytic functions on the unit disc. Even though our results appear in the folklore, detailed descriptions are hard to find, and in fact we are unable to discuss the full range of parameters. Without additional effort we work with vector-valued analytic functions, and also consider a generalized scale of function spaces, including for example so-called Q-spaces. The primary aim of this note is to generalize, and clarify, a remarkable result by Cohn and Verbitsky, on factorization of Triebel–Lizorkin spaces. Their result remains valid for functions taking values in an arbitrary Banach space, provided that the vector-valuedness “sits in the right factor”. On the other hand, if we impose vector-valuedness on the “wrong” factor, then the factorization theorem fails even for functions taking values in a separable Hilbert space.</p>}}, author = {{Rydhe, Eskil}}, issn = {{1069-5869}}, keywords = {{Factorization; Q-spaces; Triebel–Lizorkin spaces; Vector-valued analytic functions}}, language = {{eng}}, number = {{6}}, pages = {{1491--1517}}, publisher = {{Springer}}, series = {{Journal of Fourier Analysis and Applications}}, title = {{On the Characterization of Triebel–Lizorkin Type Spaces of Analytic Functions}}, url = {{http://dx.doi.org/10.1007/s00041-017-9584-0}}, doi = {{10.1007/s00041-017-9584-0}}, volume = {{24}}, year = {{2018}}, }