Radially Weighted Besov Spaces and the Pick Property

Aleman, AlexandruLund University,Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH (författare)

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.

Hartz, MichaelWashington University in St. Louis,University of Hagen (författare)
McCarthy, John E.Washington University in St. Louis (författare)
Richter, StefanUniversity of Tennessee (författare)
Matematik (naturvetenskapliga fakulteten)Matematikcentrum (creator_code:org_t)

Ingår i:Trends in MathematicsCham : Springer International Publishing, s. 29-612297-02152297-024X

Av författaren/redakt...: Aleman, Alexandr ...; Hartz, Michael; McCarthy, John E ...; Richter, Stefan

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