An Endpoint Sparse Bound for the Discrete Spherical Maximal Functions

@article{Kesler2018AnES,
  title={An Endpoint Sparse Bound for the Discrete Spherical Maximal Functions},
  author={Robert M. Kesler and Michael T. Lacey and Dar'io Mena},
  journal={arXiv: Classical Analysis and ODEs},
  year={2018}
}
  • Robert M. Kesler, Michael T. Lacey, Dar'io Mena
  • Published 2018
  • Mathematics
  • arXiv: Classical Analysis and ODEs
  • We give a short proof of some sparse bounds for the spherical maximal operator of Magyar, Stein and Wainger. This proof also includes certain endpoint estimates. The new method of proof is inspired by ones by Bourgain and Ionescu, is very efficient, and not been used in the proof of sparse bounds before. The Hardy-Littlewood Circle method is used to decompose the multiplier into major and minor arc components. The efficiency arises as one only needs a single estimate on each element of the… CONTINUE READING

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