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dc.contributor.authorMontgomery-Smith, Stephen, 1963-eng
dc.contributor.authorGeiss, Stefaneng
dc.contributor.authorSaksman, Eeroeng
dc.descriptionThe final version of this paper appears in: "Transactions of the American Mathematical Society" 362 (2010): 553-575. Print.eng
dc.description.abstractLinear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the imaginary) part of the Beurling-Ahlfors singular integral operator, acting on the X-valued Lp-space on the plane. Moreover, replacing equality by a linear equivalence, this is found to be the typical property of even multipliers. A corresponding result for odd multipliers and the Hilbert transform is given.eng
dc.relation.ispartofMathematics publications (MU)eng
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. College of Arts and Sciences. Department of Mathematicseng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
dc.subjectRiesz transformeng
dc.subject.lcshBrownian motion processeseng
dc.subject.lcshStochastic integralseng
dc.titleOn singular integral and martingale transformseng

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