TY - JOUR

T1 - Cauchy-Leray-Fantappiè integral in linearly convex domains

AU - Rotkevich, A.S.

PY - 2013

Y1 - 2013

N2 - 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 L p and BMO. Bibliography: 17 titles. © 2013 Springer Science+Business Media New York.

AB - 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 L p and BMO. Bibliography: 17 titles. © 2013 Springer Science+Business Media New York.

U2 - 10.1007/s10958-013-1558-4

DO - 10.1007/s10958-013-1558-4

M3 - Article

SP - 693

EP - 702

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -