Springer Online Journal Archives 1860-2000
Summary The author considers a schlicht pseudo-conformal mapping of a domainB in the (z 1 , z 2 )-space onto the Reinhardt circular domainC in the (ξ 1 , ξ 2 )-space by a pair of functions (see (1)§ 1). The domainB is assumed to include the bicylinder ((2)§ 2) and to omit four planes zk=ak, zk=bk, k=1, 2. Upper bounds for a sequence of the coefficients μv (k) of the developments (1) are given, see p. 304. The upper bounds depend only on ak, bk, k=1, 2, and on the radii rk of the bicylinder ((2)§ 2). The bounds are obtained by using the method of the kernel function. The result can be considered as an analogue to the inequalities of Grunsky in the theory of functions of one complex variable.
Type of Medium: