An Extrapolation of Operator Valued Dyadic Paraproducts
Abstract
We consider the dyadic paraproducts $\pi_\f$ on $\T$ associated with an $\M$valued function $\f.$ Here $\T$ is the unit circle and $\M$ is a tracial von Neumann algebra. We prove that their boundedness on $L^p(\T,L^p(\M))$ for some $1<p<\infty $ implies their boundedness on $L^p(\T,L^p(\M))$ for all $1<p<\infty$ provided $\f$ is in an operatorvalued BMO space. We also consider a modified version of dyadic paraproducts and their boundedness on $L^p(\T,L^p(\M)).
 Publication:

arXiv eprints
 Pub Date:
 September 2007
 arXiv:
 arXiv:0709.4229
 Bibcode:
 2007arXiv0709.4229M
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Classical Analysis and ODEs;
 Primary 46L52;
 Secondary;
 32C05
 EPrint:
 doi:10.1112/jlms/jdq004