Hertz potentials and asymptotic properties of massless fields

TL;DR

This paper investigates Hertz potentials for massless spin-s fields in Minkowski space, establishing existence, estimates, and peeling properties for solutions with weighted Sobolev initial data, advancing understanding of their asymptotic behavior.

Contribution

It introduces new weighted estimates for Hertz potentials and applies them to analyze asymptotic peeling properties of massless spin-s fields.

Findings

Proves existence and pointwise estimates for Hertz potentials.

Establishes weighted estimates for solutions of spin-s field equations.

Analyzes peeling properties for initial data with arbitrary weights.

Abstract

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.