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Minimum Solution of ∂k + 1 and Middle Hankel Operators

✍ Scribed by J.L.M. Wang; Z.J. Wu

Book ID
102972170
Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
531 KB
Volume
118
Category
Article
ISSN
0022-1236

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✦ Synopsis

We formulate the solution of the equation (\bar{\partial}^{k+1} F=f) with minimum (L^{2}) norm and characterize the symbol functions so that the corresponding middle Hankel operators are bounded, compact, and belong to the Schatten (p)-class ((p \geqslant 1)). This generalizes the earlier results by Peng-Rochberg-Wu. The approach is inspired by a recent work of Luecking. fi 1993 Academic Press. Inc.

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## Abstract In this paper we consider Hankel operators $ \tilde H \_{{\bar z}^k}$ = (__Id__ – __P__ ~1~)$ \bar z^k $ from __A__ ^2^(ℂ, |__z__ |^2^) to __A__ ^2,1^(ℂ, |__z__ |^2^)^⊥^. Here __A__ ^2^(ℂ, |__z__ |^2^) denotes the Fock space __A__ ^2^(ℂ, |__z__ |^2^) = {__f__: __f__ is entire and ‖__f_