Constructive description of the Besov classes in convex domains in \(\mathbb{C}^{d}\). (English. Russian original) Zbl 1430.32003
J. Math. Sci., New York 202, No. 4, 573-600 (2014); translation from Zap. Nauchn. Semin. POMI 416, 136-174 (2013).
Summary: The method of pseudoanalytic continuation developed by E. M. Dyn’kin is extended to convex domains in \(\mathbb{C}^{d}\) and used to give a constructive description of the Besov classes in such domains.
MSC:
| 32E30 | Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs |
| 32D15 | Continuation of analytic objects in several complex variables |
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
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