5 problems

Let $A$ be a dilation matrix, let $\kappa(A)$ denote its condition number, and let $\mathcal{G}(A,\psi)$ be the geometric incompatibility index associated with $A$ and a wavelet ge…

Let $a\in\mathbb{R}^d$ have positive coordinates satisfying $\sum_{j=1}^d a_j=d$. Let $K_a$ be the anisotropic kernel defined by … where $S^{d-1}$ is the unit sphere. Set…

Anisotropic Sobolev conjecture. The inequality

Endpoint asymptotic conjecture. If $T_1$ cannot be expressed as a linear combination of the other $T_j$, then

Ornstein's anisotropic non-inequality conjecture. If this estimate holds for every such $f$, then $T_1$ can be expressed as a linear combination of $T_2,\ldots,T_{\ell}$. This exte…