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In this paper we study the  L   p  ‐convergence of the Riesz means  S   R    δ  ( f ) for the sublaplacian on the sphere  S  2 n  − 1  in the complex  n ‐dimensional space ℂ  n  . We show that  S   R    δ  ( f ) converges to  f  in  L   p  ( S  2 n  − 1 ) when  δ  >  δ ( p )≔(2 n  − 1)|1/2 − 1/ p | and  R → + ∞. The index  δ ( p ) coincides with the one found by Mauceri and, with different methods, by Müller in the case of sublaplacian on the Heisenberg group. It is worth noticing that the index  δ ( p ) depends on the topological dimension of the underlying space  S  2 n −1 .

L p ‐summability of Riesz means for the sublaplacian on complex spheres