Resumen de On singular integrals of Calderón-type in Rn and BMO

Steve Hofmann

• We prove Lp (and weighted Lp) bounds for singular integrals of the form p.v. ?Rn E (A(x) - A(y) / |x - y|) (O(x - y) / |x - y|n) f(y) dy, where E(t) = cos t if O is odd, and E(t) = sin t if O is even, and where Ñ A Î BMO. Even in the case that O is smooth, the theory of singular integrals with rough kernels plays a key role in the proof. By standard techniques, the trigonometric function E can then be replaced by a large class of smooth functions F. Some related operators are also considered. As a further application we prove a compactness result for certain layer potentials.