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Radially Weighted Besov Spaces and the Pick Property

Aleman, Alexandru LU ; Hartz, Michael; McCarthy, John E. and Richter, Stefan (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:
author
organization
publishing date
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
2019-09-27 13:08:14
@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 &lt; 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 &gt; −1 the ratio ω(z)∕(1 −|z|<sup>2</sup>)<sup>α</sup> is nondecreasing for t<sub>0</sub> &lt; |z| &lt; 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},
  issn         = {2297-024X},
  keyword      = {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},
  year         = {2019},
}