Singular Integrals and Boundary Problems in Weighted Banach Function Spaces

Abstract

AbstractThe principal aim in this chapter is to indicate how singular integral operators continue to be effective tools in establishing well-posedness results for boundary problems for second-order weakly elliptic systems formulated in sufficiently flat Ahlfors regular domains and with boundary data in weighted Banach function spaces (aka, Köthe function spaces). In the first part we develop the theory of boundary layer potentials and boundary value problems in such a general functional analytic setting then, in the last part of this chapter, we specialize this discussion to the case of rearrangement invariant Banach function spaces (RIBFS for short), including Orlicz spaces, Zygmund space, Lorentz spaces, and their weighted versions.