Radially Weighted Besov Spaces and the Pick Property

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Besov space

Complete Pick space

Multiplier

Publication and Content Type

kap (subject category)

ref (subject category)