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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, Analysis and Probability Theory.
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) Published
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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: 2017-02-21Bibliographically approved

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