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Let Hn = R2n x R be the Heisenberg group with group law (x; t) (y; s) =(x + y; t + s +W(x; y))Hn = R2n x R be the Heisenberg group with group law (x; t) (y; s) =(x + y; t + s +W(x; y))x; t) (y; s) =(x + y; t + s +W(x; y)) where W is the canonical symplectic form on R2n. Let g be a measurable function on R2n with compact support , and let \nu be the Borel measure on HnW is the canonical symplectic form on R2n. Let g be a measurable function on R2n with compact support , and let \nu be the Borel measure on Hn be a measurable function on R2n with compact support , and let \nu be the Borel measure on Hn supported on the graph of the function g. Let T be the right convolution operator by \nu We are interested in studying the type set of pairs (p,q) such that our operator is bounded. This problem is well known if we replace the Heisenberg group con- volution with the ordinary convolution in R2n+1. If the graph of ' has non-zero Gaussian curvature at each point, a theorem of Littman (see [1]) implies that E. Let T be the right convolution operator by \nu We are interested in studying the type set of pairs (p,q) such that our operator is bounded. This problem is well known if we replace the Heisenberg group con- volution with the ordinary convolution in R2n+1. If the graph of ' has non-zero Gaussian curvature at each point, a theorem of Littman (see [1]) implies that ET be the right convolution operator by \nu We are interested in studying the type set of pairs (p,q) such that our operator is bounded. This problem is well known if we replace the Heisenberg group con- volution with the ordinary convolution in R2n+1. If the graph of ' has non-zero Gaussian curvature at each point, a theorem of Littman (see [1]) implies that ER2n+1. If the graph of ' has non-zero Gaussian curvature at each point, a theorem of Littman (see [1]) implies that EE is the closed triangle with vertices (0; 0), (1; 1), and (2n+1/2n+2, 1/2n+2); 0), (1; 1), and (2n+1/2n+2, 1/2n+2) (see [2]). An interesting survey of results concerning the type set for convolution operators with singular measures can be found in [3]. Returning to our setting Hn, in [4] is obtain descriptions of the type set for measures supported on curves in H1. In this talk we will give the principal ideas of the proof of Littman's theorem as well as an analogous result on the Heisenberg group for the measure supported on the graph of a canonical cuadratic form.Hn, in [4] is obtain descriptions of the type set for measures supported on curves in H1. In this talk we will give the principal ideas of the proof of Littman's theorem as well as an analogous result on the Heisenberg group for the measure supported on the graph of a canonical cuadratic form. for measures supported on curves in H1. In this talk we will give the principal ideas of the proof of Littman's theorem as well as an analogous result on the Heisenberg group for the measure supported on the graph of a canonical cuadratic form.. References [1] W. Littman. Lp �� Lq estimates for singular integral operators arising from hyperbolic equa- tions. Proc. Symp. Pure Appl. Math. AMS. 23 479-481. (1973) [2] D. Oberlin. Convolution estimates for some measures on curves. Proc. Amer. Math. Soc. 99, 1. (1987). 56-60. [3] F. Ricci. Limitatezza Lp �� Lq per operatori di convoluzione de niti da misure singolari inLp �� Lq estimates for singular integral operators arising from hyperbolic equa- tions. Proc. Symp. Pure Appl. Math. AMS. 23 479-481. (1973) [2] D. Oberlin. Convolution estimates for some measures on curves. Proc. Amer. Math. Soc. 99, 1. (1987). 56-60. [3] F. Ricci. Limitatezza Lp �� Lq per operatori di convoluzione de niti da misure singolari inProc. Symp. Pure Appl. Math. AMS. 23 479-481. (1973) [2] D. Oberlin. Convolution estimates for some measures on curves. Proc. Amer. Math. Soc. 99, 1. (1987). 56-60. [3] F. Ricci. Limitatezza Lp �� Lq per operatori di convoluzione de niti da misure singolari inConvolution estimates for some measures on curves. Proc. Amer. Math. Soc. 99, 1. (1987). 56-60. [3] F. Ricci. Limitatezza Lp �� Lq per operatori di convoluzione de niti da misure singolari inLimitatezza Lp �� Lq per operatori di convoluzione de niti da misure singolari in Rn: Bollettino U.M.I. (7) 11-A (1997), 237-252. [4] S. Secco. Lp-improving properties of measures supported on curves on the Heisenberg group.n: Bollettino U.M.I. (7) 11-A (1997), 237-252. [4] S. Secco. Lp-improving properties of measures supported on curves on the Heisenberg group.Lp-improving properties of measures supported on curves on the Heisenberg group. Studia Mathematica 132 (2) (1999).