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Let 0【p≤1.The authors give out the boundedness of δ-order Bouchner-Rieszmeans B<sub>R</sub><sup>δ</sup>（f）on the Triebel-Lizorkin spaces <sub>p</sub><sup>α,q</sup>for δ】J-2/n+1-min{α,0},where J=n/min{p,q}.Th