The Double Layer Potential Operator on Hardy Spaces

Abstract

Many studies have been done for one-dimensional Cauchy integral operator. We consider n-dimensional Cauchy integral operator for hypersurface, or we say, the double layer potential operator, and obtain the boundedness from H^p(Rⁿ) to h^p(Rⁿ) (local Hardy space). For the proof we introduce Clifford valued Hardy spaces.