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Weighted estimates for fractional maximal functions related to spherical means

  • Michael Cowling (a1), José García-Cuerva (a2) and Hendra Gunawan (a3)

Abstract

We prove weighted Lp-Lq estimates for the maximal operators ℳα, given by , where μt denotes the normalised surface measure on the sphere of centre 0 and radius t in Rd. The techniques used involve interpolation and the Mellin transform. To do this, we also prove weighted Lp-Lq estimates for the operators of convolution with the kernels |·|−α−iη.

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References

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Weighted estimates for fractional maximal functions related to spherical means

  • Michael Cowling (a1), José García-Cuerva (a2) and Hendra Gunawan (a3)

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