Weighted Herz Spaces and Regularity Results

الملخص EN

It is proved that, for the nondivergence form elliptic equations ∑i,j=1naijuxixj=f, if f belongs to the weighted Herz spaces Kpq(φ,w), then uxixj∈Kpq(φ,w), where u is the W2,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 Kpq(φ,w).