University of Birmingham > Talks@bham > Analysis Seminar > Uniform Lp-improving for dilated averages over curves

Uniform Lp-improving for dilated averages over curves

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If you have a question about this talk, please contact José Cañizo.

Numerous authors have considered the problem of determining the Lebesgue space mapping properties of the operator A given by convolution with surface measure on some smooth curve in Euclidean space. Essentially, A takes averages over translates of the curve. I will discuss a variant of this problem where averages over both translates and dilates of a fixed curve are considered. The sharp range of estimates for the resulting operator is obtained in all dimensions, except for an endpoint. The techniques used are redolent of those previously applied in the study of A. In particular, the arguments are based upon the refinement method of Christ, although significant adaptations of this method are required to fully understand the additional smoothing afforded by averaging over dilates. Some connections with weighted versions of Fourier restriction inequalities will be described.

This talk is part of the Analysis Seminar series.

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