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We prove weighted-$L^\infty$ and pointwise space-time decay estimates forweak solutions of a class of wave equations with time-independent potentialsand subject to initial data, both of low regularity, satisfying given decaybounds at infinity. The rate of their decay depends on the asymptotic behaviourof the potential and of the data. The technique is robust enough to treat alsomore regular solutions and provides decay estimates for arbitrary derivatives,provided the potential and the data have sufficient regularity, but it isrestricted to potentials of bounded strength (such that $-\Delta-|V|$ has nonegative eigenvalues).

Weighted-$L^\infty$ and pointwise space-time decay estimates for wave equations with potentials and initial data of low regularity