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New Weighted Estimates for the Disc Multiplier on Radial Functions

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Abstract

We prove a weighted estimate for the disc multiplier, acting on radial functions, at the extreme points \(p_{-}=\frac{2n}{n+1}\), extending the result of Chanillo (J Funct Anal 55:18–24, 1984). To this end, we prove a restricted weak type weighted estimate for \(p=2\) and then develop a new extrapolation result of independent interest.

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Authors and Affiliations

  1. Department of Applied Mathematics and Analysis, University of Barcelona, 08007, Barcelona, Spain

    María J. Carro

  2. School of Technology of Igualada, BarcelonaTech, Avda. Plà de la Massa, 8., 08700, Igualada, Barcelona, Spain

    Carmen Ortiz-Caraballo

Authors
  1. María J. Carro
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  2. Carmen Ortiz-Caraballo
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Corresponding author

Correspondence to María J. Carro.

Additional information

Communicated by Hans G. Feichtinger.

María J. Carro was partially supported by Grants MTM2016-75196-P (MINECO/FEDER, UE) and 2014SGR289. Carmen Ortiz-Caraballo was supported by Grant MTM2016-75196-P (MINECO/FEDER, UE).

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Carro, M.J., Ortiz-Caraballo, C. New Weighted Estimates for the Disc Multiplier on Radial Functions. J Fourier Anal Appl 25, 145–166 (2019). https://doi.org/10.1007/s00041-018-9599-1

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  • DOI: https://doi.org/10.1007/s00041-018-9599-1

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