Abstract
Properties of integral operators with weak singularities arc investigated. It is assumed that G ⊂ ℝn is a bounded domain. The boundary δG should be smooth concerning the Sobolev trace theorem. It will be proved that the integral operators and maps Wpk(G) into Wpk+1(G) and Wpk−1(G) into Wpk/p(G), respectively, and are bounded. Here θ ∈ S ⊂ ℝn, where S is the unit sphere. Furthermore, f possesses bounded first order derivatives and is bounded on S. Then applications to first order systems are discussed.
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