m-isometric commuting tuples of operators on a Hilbert space

We consider a generalization of isometric Hilbert space operators to the multivariable setting. We study some of the basic properties of these tuples of commuting operators and we explore several examples. In par-ticular, we show that the d-shift, which is important in the dilation theory of d-contractions (or row contractions), is a d-isometry. As an application of our techniques we prove a theorem about cyclic vectors in certain spaces of analytic functions that are properly contained in the Hardy space of the unit ball of Cd.