The restriction-extension operator on Lebesgue spaces with symmetries and applications to the limiting absorption principle

Abstract We prove sharp $$L^p$$ - $$L^q$$ -estimates for the Restriction-Extension operator acting on block-radial functions with the aid of new oscillatory integral estimates and interpolation results in mixed Lorentz spaces. We apply this to the Limiting Absorption Principle for elliptic (pseudo-)differential operators with constant coefficients. In this way we obtain a richer existence theory for Helmholtz-type problems on $$\mathbb {R}^d$$ with block-radial right hand sides.