@inbook{f49df3b9ed1546a281aed9d9d02b89ba,

title = "Radially Weighted Besov Spaces and the Pick Property",

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.",

keywords = "Besov space, Complete Pick space, Multiplier",

author = "Alexandru Aleman and Michael Hartz and McCarthy, {John E.} and Stefan Richter",

note = "Funding Information: M.H. was partially supported by a Feodor Lynen Fellowship. J.M. was partially supported by National Science Foundation Grant DMS 1565243. Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

doi = "10.1007/978-3-030-14640-5_3",

language = "English",

series = "Trends in Mathematics",

publisher = "Springer International Publishing",

pages = "29--61",

booktitle = "Trends in Mathematics",

}