Integer part polynomial correlation sequences

Following an approach presented by N. Frantzikinakis, we prove that any multiple correlation sequence, defined by invertible measure preserving actions of commuting transformations with integer part polynomial iterates, is the sum of a nilsequence and an error term, small in uniform density. As an intermediate result, we show that multiple ergodic averages with iterates given by the integer part of real valued polynomials converge in the mean. Also, we show that under certain assumptions the limit is zero. An important role in our arguments plays a transference principle, communicated to us by M. Wierdl, that enables to deduce results for $\mathbb{Z}$-actions from results for flows.