Abstract. Asymptotics is obtained for the Lebesgue constants of the Cesàro means of spherical harmonic expansions. Precise constant in the main term is found and the order of growth of the remainder term is given.

AMS Subject Classification (1991): 42C10, 43A90, 33D55, 442B08

Received March 17, 1997 and in revised form June 9, 1997. (Registered under 2657/2009.)