The Stokes Operator in Weighted $L^{q}$-Spaces I: Weighted Estimates for the Stokes Resolvent Problem in a Half Space

Abstract.

In this paper we derive weighted $L^{q}$-estimates for the Stokes resolvent system in the half space for weights of Muckenhoupt class, on which a new approach to maximal $L^{p}$-regularity of the Stokes operator for the half space and a bounded domain in weighted $L^{q}$-spaces in the forthcoming part II is based. We stress that our results hold for general Muckenhoupt weights. In particular, the weights may tend to zero or become singular at the boundary of the domain.