Byczkowski, Tomasz; Graczyk, Piotr Malliavin calculus for stable processes on Heisenberg group. (English) Zbl 0785.60028 Probab. Math. Stat. 13, No. 2, 277-292 (1992). Malliavin’s calculus for symmetric stable semigroups and truncated stable semigroups of measures on the Heisenberg group is investigated. In particular, \(C^ \infty\)-smoothness is obtained for truncated stable semigroups of the class \(C^ 1\) with a compact support, and, more generally, for densities of the same class \(C^ 1\) which rapidly decrease at infinity. Reviewer: A.Yu.Veretennikov (Moskva) Cited in 1 ReviewCited in 1 Document MSC: 60H07 Stochastic calculus of variations and the Malliavin calculus 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization Keywords:stable semigroups of measures; Malliavin’s calculus; stable semigroups; Heisenberg group PDFBibTeX XMLCite \textit{T. Byczkowski} and \textit{P. Graczyk}, Probab. Math. Stat. 13, No. 2, 277--292 (1992; Zbl 0785.60028)