Mathematics – Classical Analysis and ODEs
Scientific paper
2003-10-21
Mathematics
Classical Analysis and ODEs
22 pages, 13 references. Paper to appear in Houston Journal of Math. Small changes to the manuscript
Scientific paper
$H^2\zProd$ 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 Journ\'e \cite{MR87g:42028}, which occurs implicitly in the work of J. Pipher \cite{MR88a:42019}.
Lacey Michael T.
Terwilleger Erin
No associations
LandOfFree
Hankel Operators in Several Complex Variables and Product $BMO\zProd$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hankel Operators in Several Complex Variables and Product $BMO\zProd$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hankel Operators in Several Complex Variables and Product $BMO\zProd$ will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-665559