The Helmholtz decomposition in weighted L^p spaces in cones

In this paper we prove the Helmholtz decomposition in conical domains of $R^3$ in weighted $L^p_\beta$ spaces under a spectral condition on $\beta, p$. The basic bricks are the transformation of the original problem into a problem set in cylindrical domains and the combination of a priori bounds from [5] with the vector-valued multiplier theorem [29]