R-sectoriality of truly cylindrical boundary value problems

Abstract

We prove R-sectoriality or, equivalently, L ^p-maximal regularity for a class of operators on some cylindrical domains of the form ℝ^n-k x V, where V ⊂ ℝ^k is a domain with compact boundary, ℝ^k, or a half-space. Instead of extensive localization procedures, we present an elegant approach via operator valued multiplier theory, which takes advantage of the cylindrical shape of both, the domain and the operator.