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In this paper, we show that the Bochner-Riesz means are bounded on weighted and variable Hardy spaces by using the finite atomic decomposition theories. The boundedness of Bochner-Riesz means on weighted and variable Carleson measure spaces is also obtained. Moreover, we also prove that the maximal Bochner-Riesz means are bounded from weighted or vaiable Hardy spaces to weighted or variable Lebesgue spaces. Mathematics subject classification (2010): 42B25, 42B30, 46E30.

Some Hardy and Carleson measure spaces estimates for Bochner-Riesz means