Radially Weighted Besov Spaces and the Pick Property
(2019) In Trends in Mathematics p.2961 Abstract
For s∈ ℝ the weighted Besov space on the unit ball B_{d} of ℂ^{d} is defined by (Formula presented.). Here R^{s} 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 t_{0} < 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:
http://lup.lub.lu.se/record/662de4ac8f6347d58144a4b1f282223c
 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
 2297024X
 22970215
 DOI
 10.1007/9783030146405_3
 language
 English
 LU publication?
 yes
 id
 662de4ac8f6347d58144a4b1f282223c
 date added to LUP
 20190625 12:41:41
 date last changed
 20190927 13:08:14
@inbook{662de4ac8f6347d58144a4b1f282223c, 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}, issn = {2297024X}, keyword = {Besov space,Complete Pick space,Multiplier}, language = {eng}, pages = {2961}, publisher = {Springer}, series = {Trends in Mathematics}, title = {Radially Weighted Besov Spaces and the Pick Property}, url = {http://dx.doi.org/10.1007/9783030146405_3}, year = {2019}, }