On transfer inequalities in Diophantine approximation

Abstract

Let $\Theta$ be a point in ${\mathbf{R}}^n$. We split the classical Khintchine's Transference Principle into $n-1$ intermediate estimates which connect exponents ${\omega }_d(\Theta )$ measuring the sharpness of the approximation to $\Theta$ by linear rational varieties of dimension $d$, for $0\le d\le n-1$. We also review old and recent results related to these $n$ exponents.