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2017 Anisotropic Ornstein noninequalities
Krystian Kazaniecki, Dmitriy M. Stolyarov, Michał Wojciechowski
Anal. PDE 10(2): 351-366 (2017). DOI: 10.2140/apde.2017.10.351

Abstract

We investigate the existence of a priori estimates for differential operators in the L1 norm: for anisotropic homogeneous differential operators T1,,T, we study the conditions under which the inequality

T1fL1(d) j=2T jfL1(d)

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.

Citation

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Krystian Kazaniecki. Dmitriy M. Stolyarov. Michał Wojciechowski. "Anisotropic Ornstein noninequalities." Anal. PDE 10 (2) 351 - 366, 2017. https://doi.org/10.2140/apde.2017.10.351

Information

Received: 26 January 2016; Revised: 6 October 2016; Accepted: 14 November 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1362.35013
MathSciNet: MR3619873
Digital Object Identifier: 10.2140/apde.2017.10.351

Subjects:
Primary: 26B25 , 26B35

Keywords: Bellman function , martingale transform , Ornstein noninequalities

Rights: Copyright © 2017 Mathematical Sciences Publishers

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