A T1 theorem and Calderón–Zygmund operators in Campanato spaces on domains

Abstract

AbstractGiven a Lipschitz domain , a Calderón–Zygmund operator T and a modulus of continuity , we solve the problem when the truncated operator sends the Campanato space into itself. The solution is a T1 type sufficient and necessary condition for the characteristic function of D: urn:x-wiley:0025584X:media:mana201700488:mana201700488-math-0006To check the hypotheses of T1 theorem we need extra restrictions on both the boundary of D and the operator T. It is proved that the truncated Calderón–Zygmund operator with an even kernel is bounded on , provided D is a ‐smooth domain.