| Title | Single point extremal functions in Bergman-type spaces |
| Authors | Alexandru Aleman, S Richter |
| Alternative Location | http://dx.doi.org/10.1512/i..., Restricted Access |
| Publication | Indiana University Mathematics Journal |
| Year | 2002 |
| Volume | 51 |
| Issue | 3 |
| Pages | 581 - 605 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Indiana University |
| Abstract English | Let A be a zero sequence for the Bergman space L-a(2) of the unit disc D, and let phi(A) be the corresponding canoniacal zero divisor. In this paper we consider quotients of the type phi(Au {alpha})/phi(A), alpha is an element of D. By use of methods from the theory of reproducing kernels we shall show that the modulus of such functions is always bounded by 3, and that they can be written as a product of a single Blaschke factor and a function whose real part is greater than 1. Our methods apply in somewhat larger generality. In particular, our results lead to a new proof of the contractive zero-divisor property in weighted Bergman spaces with logarithmically subharmonic weights. For the unweighted Bergman spaces L-a(p), 0 < p < infinity, we show that the canonical zero divisor phi(A) for a zero sequence with n elements can be written as a product of n starlike functions. |
| Keywords | Bergman spaces, contractive divisors, |
| ISBN/ISSN/Other | ISSN: 0022-2518 |
Questions: webmaster
Last update: 2013-04-11
Centre for Mathematical Sciences, Box 118, SE-22100, Lund. Telefon: +46 46-222 00 00 (vx)