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We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the norm of the solution in terms of the energy. We also characterise the maximisers.
We prove a Calderón-Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators, generalized Radon transforms and singular oscillatory integrals.
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