Weighted estimates for maximal functions associated with finite type curves in R2

Abstract In this paper we establish weighted estimates for the maximal function associated with the finite type curve in the plane R 2 . We follow an approach used by M. Lacey to obtain sparse bounds for the maximal function. Further, using a different approach we obtain a characterisation of power weights for the weighted L p boundedness of the maximal function. We also obtain analogous results for the lacunary maximal function associated with the finite type curve in the plane R 2 .

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