In 1934, G. H. Hardy and J. E. Littlewood calculated [Proc. London Math. Soc. (2) 36 (1934), pp. 516–531] the optimal Cesàro exponent for Hardy spaces. In this paper we calculate it for mixed norm spaces, hence including the Bergman spaces in particular. The main technical challenge lies in the analysis of the example needed for the critical case. [ABSTRACT FROM AUTHOR]