Cauchy–Leray–Fantappiè integral in linearly convex domains

Abstract

An important tool in analysis of functions of one complex variable is the Cauchy formula. However, in the case of several complex variables there is no unique and convenient formula of this sort. One can use the Szegö projection S, but the kernel of the operator S has usually no closed form expression. Another choice is the Cauchy–Leray–Fantappiè formula that has a rather closed form kernel for large classes of domains. In this paper, we prove the boundedness of the Cauchy–Leray–Fantappiè integral for linearly convex domains as an operator on Lp and BMO. Bibliography: 17 titles.