Radially Weighted Besov Spaces and the Pick Property
(2019) In Trends in Mathematics p.29-61- Abstract
For s∈ ℝ the weighted Besov space on the unit ball Bd of ℂd is defined by (Formula presented.). Here Rs is a power of the radial derivative operator (Formula presented.), V denotes Lebesgue measure, and ω is a radial weight function not supported on any ball of radius < 1. Our results imply that for all such weights ω and ν, every bounded column multiplication operator (Formula presented.) induces a bounded row multiplier (Formula presented.). Furthermore we show that if a weight ω satisfies that for some α > −1 the ratio ω(z)∕(1 −|z|2)α is nondecreasing for t0 < |z| < 1, then (Formula presented.) is a complete Pick space, whenever s ≥ (α + d)∕2.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/662de4ac-8f63-47d5-8144-a4b1f282223c
- author
- Aleman, Alexandru LU ; Hartz, Michael ; McCarthy, John E. and Richter, Stefan
- organization
- publishing date
- 2019
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Besov space, Complete Pick space, Multiplier
- host publication
- Trends in Mathematics
- series title
- Trends in Mathematics
- pages
- 33 pages
- publisher
- Springer
- external identifiers
-
- scopus:85066734560
- ISSN
- 2297-024X
- 2297-0215
- DOI
- 10.1007/978-3-030-14640-5_3
- language
- English
- LU publication?
- yes
- id
- 662de4ac-8f63-47d5-8144-a4b1f282223c
- date added to LUP
- 2019-06-25 12:41:41
- date last changed
- 2024-07-09 18:51:48
@inbook{662de4ac-8f63-47d5-8144-a4b1f282223c, abstract = {{<p>For s∈ ℝ the weighted Besov space on the unit ball B<sub>d</sub> of ℂ<sup>d</sup> is defined by (Formula presented.). Here R<sup>s</sup> is a power of the radial derivative operator (Formula presented.), V denotes Lebesgue measure, and ω is a radial weight function not supported on any ball of radius < 1. Our results imply that for all such weights ω and ν, every bounded column multiplication operator (Formula presented.) induces a bounded row multiplier (Formula presented.). Furthermore we show that if a weight ω satisfies that for some α > −1 the ratio ω(z)∕(1 −|z|<sup>2</sup>)<sup>α</sup> is nondecreasing for t<sub>0</sub> < |z| < 1, then (Formula presented.) is a complete Pick space, whenever s ≥ (α + d)∕2.</p>}}, author = {{Aleman, Alexandru and Hartz, Michael and McCarthy, John E. and Richter, Stefan}}, booktitle = {{Trends in Mathematics}}, issn = {{2297-024X}}, keywords = {{Besov space; Complete Pick space; Multiplier}}, language = {{eng}}, pages = {{29--61}}, publisher = {{Springer}}, series = {{Trends in Mathematics}}, title = {{Radially Weighted Besov Spaces and the Pick Property}}, url = {{http://dx.doi.org/10.1007/978-3-030-14640-5_3}}, doi = {{10.1007/978-3-030-14640-5_3}}, year = {{2019}}, }