Some improved $L^2$ fractal-type inequalities are obtained for the wave equation, using the analogue of the Du-Zhang method for the Schr\"odinger equation. These improve the known decay rates of conical averages for the Fourier transform of measures, in dimensions $d \geq 4$.
Some inequalities for the Fourier transform and their limiting behaviour
Improved decay rates with small regularity loss for the wave equation about a Schwarzschild black hole
Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to Linear Parabolic and (Hypo-)Elliptic PDEs
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