Anisotropic Ornstein non inequalities

Abstract

We investigate existence of a priori estimates for differential operators in $L^1$ norm: for anisotropic homogeneous differential operators $T_1,\dots ,T_{\ell }$, we study the conditions under which the inequality $$\Vert T_{1}f{\Vert }_{L_1({\mathbb{R}}^d)}\lesssim \sum _{j=2}^{\ell }\Vert T_{j}f{\Vert }_{L_1({\mathbb{R}}^d)}$$ holds true. We also discuss a similar problem for martingale transforms.

15 pages

References in corpus (1)

• On Rank-One Convex Functions that are homogeneous of Degree One

Cited by in corpus (1)

• Remarks on Ornstein's non-inequality in ${\mathbb{R}}^{2\times 2}$