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Weighted estimates for maximal functions associated with finite type curves in R2
Nonlinear Analysis ( IF 1.4 ) Pub Date : 2020-12-17 , DOI: 10.1016/j.na.2020.112225 Ramesh Manna , Saurabh Shrivastava , Kalachand Shuin
中文翻译:
与有限类型曲线相关的最大函数的加权估计
更新日期:2020-12-17
Nonlinear Analysis ( IF 1.4 ) Pub Date : 2020-12-17 , DOI: 10.1016/j.na.2020.112225 Ramesh Manna , Saurabh Shrivastava , Kalachand Shuin
In this paper we establish weighted estimates for the maximal function associated with the finite type curve in the plane . 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 boundedness of the maximal function. We also obtain analogous results for the lacunary maximal function associated with the finite type curve in the plane .
中文翻译:
与有限类型曲线相关的最大函数的加权估计
在本文中,我们为与平面中有限类型曲线相关的最大函数建立了加权估计 。我们遵循M.Lacey使用的方法来获得最大函数的稀疏边界。此外,使用不同的方法,我们获得了加权的功率权重的表征最大函数的有界性。我们还获得了与平面中有限类型曲线相关的基元极大函数的类似结果。