  We prove $L^p$-$L^q$-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. Similar techniques apply to
the Limiting Absorption Principles for certain 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.
