Spaces of Holomorphic Functions in the Unit Ball

By Kehe Zhu. 2005

1,300 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/c8467b95012103cb35323658495b9a43363b8018

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Free holomorphic functions on the unit ball of B(H)n (2006, background): “In Section 9, we introduce a pseudohyperbolic metric d on [B(H)n]1 which is invariant under the action of the free holomorphic automorphism group of [B(H)n]1 and turns out to be a noncommutative extension of the pseudohyperbolic distance (see [56]) on Bn, the open unit ball of C, i.”
Toeplitz operators and Carleson measures in strongly pseudoconvex domains (2012, background): “[38] K. Zhu, Spaces of holomorphic functions in the unit ball.”
Carleson Measures and Toeplitz operators for weighted Bergman spaces on the unit ball (2014, background): “30 in [28] that, for any sequence of real numbers {λk} ∈ p1 , the function ft (z) = ∞ ∑ k=1 λkrk(t) (1 − |ak|2)n+1+β−(n+1+α1)/p1 (1 − 〈z, ak〉)n+1+β is in A1 α1 with ‖ft‖p1,α1 ‖{λk}‖ p1 for almost every t in (0,1).”
Taylor coefficients and coefficient multipliers of Hardy and Bergman-type spaces (2016, background): “Some facts are stated without proof but these can be found in a number of monographs on Hardy spaces and related topics such as [3]–[8].”
Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_\alpha ^p$ (2011, neutral): “It is well known (see [24]) that ρ is indeed a metric on Bn and that ρ satisfies the identity 1− (ρ(z, w))(2) = (1− |z| 2)(1− |w|2) |1− z · w| .”
Weighted Composition Operators from H∞ to the Bloch Space of a Bounded Homogeneous Domain (2010, methodology): “1 of [32], the following useful formula for calculating the Bloch seminorm of a function f ∈ B(Bn) was given.”
Riemann–Stieltjes-type integral operators on the unit ball in (2007, background): “Suppose that f 2 B 0 , by a well-known theorem (see, for example [19]), we know that f 2 B 0 if and only if lim z!@B 1 jzj(2) jrfðzÞj 1⁄4 0:”
Volterra type integration operators from Bergman spaces to Hardy spaces (2019, background): “48 of [37]).”
Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls (2007, background): “For σ n/2 we are in the realm of the classical Hardy and Bergman spaces and the description of the Carleson measures is well established [27,33].”
The corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in $\C^n$ (2008, background): “17 of [21] shows that ( 1 − |z|(2) )l ∂ ∂zl ( ∂ ∂zk f ) (z) ∈ L ( νp(|k|+σ)−n−1 ) , which shows that (2) follows from (1).”