Bianalytic capacities and Calderon commutators
- 30 Downloads
Bianalytic capacities appear naturally in problems of uniform approximation of functions by bianalytic functions on compact sets in the complex plane. They play a crucial role in constructions of approximants in several such problems. It turns out, that bianalytic capacities obey several unusual properties in comparison with other capacities studied in the approximation theory. In particular, bianalytic capacities do not satisfy the semiadditivity property. In this paper, we study these capacities and consider their relations with Calderon commutators.
KeywordsSingular integrals Calderon commutators Carleson measures Lipschitz graphs Littlewood–Paley theory Capacities Semiadditivity property Bianalytic functions Uniform approximation
Compliance with ethical standards
Conflict of interest
There is no conflicts of interests.
- 17.Dyn’kin, E.M.: Methods of the theory of singular integrals. II. The Littlewood-Paley theory and its applications, commutative harmonic analysis, IV. In: Khavin, V.P., Nikol’skiy, N.K. (eds.) Encyclopaedia Mathematical Science, vol. 42, pp. 97–194. Springer, Berlin (1992)Google Scholar