Convolution operators with singular measures of fractional type on the Heisenberg group

We consider the Heisenberg group H-n = C-n x R. Let mu(gamma) be the fractional Borel measure on H-n defined by mu(gamma) (E) = integral(Cn) chi E(w, phi(w)) Pi(n)(j=1) eta(j)(vertical bar w(j)vertical bar(2))vertical bar wj vertical bar(-gamma/n) dw, where 0 < gamma < 2n, phi(w) = Sigma(n)(j=1) a(j)vertical bar jw(j)vertical bar(2), w = (w1 , ... , wn) is an element of C-n, a(j) is an element of R, and eta(j) is an element of C-c(infinity)(R). In this paper we study the set of pairs (p, q) such that right convolution with mu(gamma) is bounded from L-p(H-n) into L-q(H-n).