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In this paper we study the bounded property of the Riesz means for the eigenfunction expansions for elliptic operators on the Hardy spaces. Our result generalizes the classical result due to Sjölin and Stein-Taibleson-Weiss on the Bochner-Riesz means.

The $H\sp p$-boundedness of the Riesz means for the eigenfunction expansions for elliptic operators with constant coefficients