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Bounds for partial derivatives: necessity of UMD and sharp constants
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Univ Helsinki, Gustaf Hallstromin Katu 2b, FIN-00014 Helsinki, Finland..
2016 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 282, no 3-4, 635-650 p.Article in journal (Refereed) PublishedText
Abstract [en]

We prove the necessity of the UMD condition, with a quantitative estimate of the UMD constant, for any inequality in a family of bounds between different partial derivatives of . In particular, we show that the estimate characterizes the UMD property, and the best constant K is equal to one half of the UMD constant. This precise value of K seems to be new even for scalar-valued functions.

Place, publisher, year, edition, pages
2016. Vol. 282, no 3-4, 635-650 p.
Keyword [en]
Partial derivative, Fourier multiplier, Sharp constant, UMD property, Martingale inequality, Transference
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-286645DOI: 10.1007/s00209-015-1556-yISI: 000372303100002OAI: oai:DiVA.org:uu-286645DiVA: diva2:923832
Available from: 2016-04-27 Created: 2016-04-21 Last updated: 2016-04-27Bibliographically approved

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Castro, Alejandro J.
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