Radially Weighted Besov Spaces and the Pick Property

Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

9 Scopus citations


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.

Original languageEnglish
Title of host publicationTrends in Mathematics
PublisherSpringer International Publishing
Number of pages33
StatePublished - 2019

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X


  • Besov space
  • Complete Pick space
  • Multiplier


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