منابع مشابه
Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball
Let BN be the unit ball in the N-dimensional complex space, for ψ, a holomorphic function in BN , and φ, a holomorphic map from BN into itself, the weighted composition operator on the weighted Hardy space H(β,BN ) is given by (Cψ,φ) f = ψ(z) f (φ(z)), where f ∈H2(β,BN ). This paper discusses the spectrum of Cψ,φ when it is compact on a certain class of weighted Hardy spaces and when the compos...
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متن کاملSome New Observations on Interpolation in the Spectral Unit Ball
We present several results associated to a holomorphic-interpolation problem for the spectral unit ball Ωn, n ≥ 2. We begin by showing that a known necessary condition for the existence of a O(D; Ωn)-interpolant (D here being the unit disc in C), given that the matricial data are non-derogatory, is not sufficient. We provide next a new necessary condition for the solvability of the two-point in...
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We solve a bitangential interpolation problem for contractive multipliers on the Arveson space with an arbitrary interpolating set in the closed unit ball B of C. The solvability criterion is established in terms of positive kernels. The set of all solutions is parametrized by a Redheffer transform. Mathematics Subject Classification (2000). Primary 47A57; Secondary 30E05.
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A bounded linear operator that maps H to L and L to L is bounded from L to L for each p ∈ (1, 2), by a famous interpolation result of Fefferman and Stein. We prove L-norm bounds that grow like O ( 1/(p− 1) ) as p ↓ 1. This growth rate is optimal, and improves significantly on the previously known exponential bound O(21/(p−1)).
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1987
ISSN: 1385-7258
DOI: 10.1016/1385-7258(87)90021-7