An extrapolation principle for the Fourier operator

With Miquel Saucedo (Centre de Recerca Matemàtica (CRM), Barcelona)

An extrapolation principle for the Fourier operator

In this talk we will discuss some situations in which a Fourier inequality (including the classical Hausdorff-Young and Hardy-Littlewood estimates) can be extended to a broader class of operators. We will also see how this can be used to solve two classical problems: the Bernstein problem of absolute convergence of Fourier series and the characterization of Fourier inequalities with monotonic weights.

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