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15 August 2020
 
  » arxiv » 1505.5416

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Anisotropic Ornstein non inequalities
Krystian Kazaniecki ; Dmitriy M. Stolyarov ; Michal Wojciechowski ;
Date 20 May 2015
AbstractWe 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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