Abstract
This paper deals with holomorphic functions from Bergman spaces Bp in the disk and provides the existence of deformations (variations) which do not increase the norm of functions and preserve some other prescribed properties. Admissible variations are constructed (for even integer p ≥ 2) using special quasiconformal maps of the complex plane (in line with a new approach to variational problems for holomorphic functions in Banach spaces).
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