UNIVERSITY OF WISCONSIN-MADISON CENTER FOR THE MATHEMATICAL SCIENCES A multivariate form of Hardy's inequality and Lp-error bounds for multivariate Lagrange interpolation schemes

valid for f 2 Lp(IR ) and an arbitrary nite sequence of points in IR, is discussed. The linear functional f 7! R f was introduced by Micchelli [M80] in connection with Kergin interpolation. This functional also naturally occurs in other multivariate generalisations of Lagrange interpolation, including Hakopian interpolation, and the Lagrange maps of Section 5. For each of these schemes, (1) implies Lp-error bounds. We discuss why (1) plays a crucial role in obtaining Lp-bounds from pointwise integral error formul for multivariate generalisations of Lagrange interpolation.