An energy-based approach to weighted L¹ to L∞ estimates for the wave operator

We present a proof of an L¹ to L∞ estimate for radial solutions to the inhomogeneous wave equation in three spatial dimensions. Similar estimates trace back to the work of Hörmander and Klainerman, and later, Keel, Smith, and Sogge. The novelty in our estimate is in the method of proof, which arrives at the L¹ to L∞ bound using the integrated local energy estimates of Metcalfe and Rhoads, along with spacetime Klainerman-Sobolev decay estimates of Metcalfe, Tataru, and Tohaneanu.