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Young Women in Harmonic Analysis and PDE

December 2-4, 2016

Dominique Maldague (UC Berkeley)

A restricted extremization problem for a weakened Hausdorff-Young inequality

Among subsets of Euclidean space with prescribed measure, for which functions and sets is the L^q norm of the Fourier transform of bounded multiples of the indicator function maximized? Various partial results concerning this question are established, including the existence of maximizers and the identification of maximizers as ellipsoids times Fourier characters for certain exponents.