Commutators and Localization on the Drury-arveson Space
نویسندگان
چکیده
Let f be a multiplier for the Drury-Arveson space H n of the unit ball, and let ζ1, ..., ζn denote the coordinate functions. We show that for each 1 ≤ i ≤ n, the commutator [M∗ f ,Mζi ] belongs to the Schatten class Cp, p > 2n. This leads to a localization result for multipliers.
منابع مشابه
On the Problem of Characterizing Multipliers for the Drury-arveson Space
Let H n be the Drury-Arveson space on the unit ball B in C , and suppose that n ≥ 2. Let kz, z ∈ B, be the normalized reproducing kernel for H n. In this paper we consider the following rather basic question in the theory of the Drury-Arveson space: For f ∈ H n, does the condition sup|z|<1 ‖fkz‖ < ∞ imply that f is a multiplier of H n? We show that the answer is negative. We further show that t...
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