Radially Weighted Besov Spaces and the Pick Property

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 t₀ < |z| < 1, then (Formula presented.) is a complete Pick space, whenever s ≥ (α + d)∕2.