This is an announcement for the paper "Estimates of disjoint sequences in Banach lattices and r. i. function spaces" by R. Gonzalo and J. A. Jaramillo. Abstract: We introduce UDSp-property (resp. UDTq-property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lattices, in the sense of the existence of differentiable bump functions. Archive classification: Functional Analysis Mathematics Subject Classification: 46B42; 46E30; 46G05 The source file(s), disjoint.tex: 39217 bytes, is(are) stored in gzipped form as 0404526.gz with size 12kb. The corresponding postcript file has gzipped size 64kb. Submitted from: jaramil@mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404526 or http://arXiv.org/abs/math.FA/0404526 or by email in unzipped form by transmitting an empty message with subject line uget 0404526 or in gzipped form by using subject line get 0404526 to: math@arXiv.org.