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20 April 2024

» arxiv » 1505.5416

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Anisotropic Ornstein non inequalities
Krystian Kazaniecki ; Dmitriy M. Stolyarov ; Michal Wojciechowski ;
Date:	20 May 2015
Abstract:	We investigate existence of a priori estimates for differential operators in $L^1$ norm: for anisotropic homogeneous differential operators $T_1, ldots , T_{ell}$, we study the conditions under which the inequality $$ \|T_1 f\|_{L_1(mathbb{R}^d)} lesssim sumlimits_{j = 2}^{ell}\|T_j f\|_{L_1(mathbb{R}^d)} $$ holds true. We also discuss a similar problem for martingale transforms.
Source:	arXiv, 1505.5416
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