Abstract
The work is devoted to the proof of a new L ∞ − L 2 {L^\infty } - {L^2} weighted estimate for the solution to the nonhomogeneous wave equation in ( 3 + 1 ) \left ( {3 + 1} \right ) -dimensional space-time. The weighted Sobolev spaces are associated with the generators of the Poincaré group. The estimate obtained is applied to prove the global existence of a solution to a nonlinear system of wave and Klein-Gordon equations with small initial data.
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