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Using the extrapolation of one-sided weights, we establish the boundedness ofcommutators generated by weighted Lipschitz functions and one-sided singularintegral operators from weighted Lebesgue spaces to weighted one-sidedTriebel-Lizorkin spaces. The corresponding results for commutators of one-sideddiscrete square functions are also obtained.

Weighted Lipschitz estiamtes for commutators of one-sided operators on one-sided Triebel-Lizorkin spaces