Hankel Operators in Several Complex Variables and Product $BMO\zProd$

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dc.creatorLacey, Michael T
dc.creatorTerwilleger, Erin
dc.date2003-10-21
dc.date2007-04-05
dc.date.accessioned2026-07-07T07:54:53Z
dc.date.available2026-07-07T07:54:53Z
dc.description$H^2\zProd$ denotes the Hardy space of square integrable functions analytic in each variable separately. Let $P^{\ominus}$ be the natural projection of $L^2\zProd$ onto $\z8{H^2\zProd}$. A Hankel operator with symbol $b$ is the linear operator from $H^2\zProd$ to $\z8{H^2\zProd}$ given by $H_b \zvf=P^{\ominus}\bar b \zvf$. We show that \md0 \norm H_b ..\simeq \norm P^{\oplus}b.BMO\zProd., \emd where the right hand norm is S.-Y. Chang and R. Fefferman product $BMO$. This fact has well known equivalences in terms of commutators and the weak factorization of $H^1\zProd$. In the case of two complex variables, this is due to Ferguson and Lacey \cite{MR1961195}. While the current proof is inductive, and one can take the one complex variable case as the basis step, it is heavily influenced by the methods of Ferguson and Lacey. The induction is carried out with a particular form of a lemma due to Journé \cite{MR87g:42028}, which occurs implicitly in the work of J. Pipher \cite{MR88a:42019}.
dc.description22 pages, 13 references. Paper to appear in Houston Journal of Math. Small changes to the manuscript
dc.identifierhttps://arxiv.org/abs/math/0310348
dc.identifierhttp://arxiv.org/abs/math/0310348
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126780
dc.subjectClassical Analysis and ODEs
dc.subjectOperator Algebras
dc.titleHankel Operators in Several Complex Variables and Product $BMO\zProd$
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