Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents

Abstract

We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting. We also provide applications to inhomogeneous Diophantine approximation on manifolds and to weighted badly approximable vectors. Finally, we interpret and prove a conjecture of Beresnevich-Velani (2010) about inhomogeneous intermediate exponents.

Minor revisions following referee report. This is the final version. To appear in Annali Della Scuola Normale Superiore Di Pisa