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MR1198458 35P05 (35J30 42B30)
Liu, He Ping; Lu, Shan Zhen The $H^p$-boundedness of the Riesz means for the eigenfunction expansions for elliptic operators with constant coefficients. Proc. Amer. Math. Soc. 122 (1994), no. 2, 487–494.
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