HARDY AND RELLICH-TYPE INEQUALITIES WITH REMAINDERS FOR BAOUENDI-GRUSHIN VECTOR FIELDS

摘要

In this paper we study Hardy and Rellich-type inequalities and their improved versions for the Baouendi-Grushin vector fields : del(gamma) = (del(x), vertical bar x vertical bar(gamma)del(y)) where gamma > 0, del(x) and del(y) are usual gradient operators in the variables x is an element of R-m and y is an element of R-k, respectively. We also obtain sharp constants for these inequalities. Furthermore, we prove a sharp uncertainty principle inequality for the Baouendi-Grushin vector fields.