Hertz potentials and asymptotic properties of massless fields

Understand

In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces.

• We prove existence and pointwise estimates for the Hertz potentials using a weighted estimate for the wave equation.
• This is then applied to give weighted estimates for the solutions of the spin-s field equations, for arbitrary half-integer s.
• In particular, the peeling properties of the free massless spin-s fields are analyzed for initial data in weighted Sobolev spaces with arbitrary, non-integer weights.