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Anisotropic Ornstein
noninequalities
Krystian Kazaniecki, Dmitriy M. Stolyarov and Michał Wojciechowski |
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Vol. 10 (2017), No. 2, 351–366
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Abstract |
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We investigate the existence of a priori estimates for differential operators in the norm: for anisotropic homogeneous differential operators , we study the conditions under which the inequality holds true. Properties of homogeneous rank-one convex functions play the major role in the subject. We generalize the notions of quasi- and rank-one convexity to fit the anisotropic situation. We also discuss a similar problem for martingale transforms and provide various conjectures. |
Keywords
Ornstein noninequalities, Bellman function, martingale
transform
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Mathematical Subject Classification 2010
Primary: 26B35, 26B25
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Milestones
Received: 26 January 2016
Revised: 6 October 2016
Accepted: 14 November 2016
Published: 23 February 2017
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Authors |
| Krystian Kazaniecki | ||
| Institute of Mathematics University of Warsaw Warsaw Poland |
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| Dmitriy M. Stolyarov | ||
| Institute of Mathematics Polish Academy of Sciences Warsaw Poland |
P. L. Chebyshev Research
Laboratory St. Petersburg State University St. Petersburg Russia |
St. Petersburg Department of Steklov
Mathematical Institute Russian Academy of Sciences St. Petersburg Russia |
| Michał Wojciechowski | ||
| Institute of Mathematics Polish Academy of Sciences Warsaw Poland |
Institute of Mathematics University of Warsaw Warsaw Poland |
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