Weighted Herz Spaces and Regularity Results

It is proved that, for the nondivergence form elliptic equations Sigma(n)(i,j-1) a(ij)u(xixj) = f, if f belongs to the weighted Herz spaces K-q(p)(phi, w), then u(xixj) is an element of K-q(p)(phi, w), where u is the W-2,W-p-solution of the equations. In order to obtain this, the authors first establish the weighted boundedness for the commutators of some singular integral operators on K-p(q)(phi, w).