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Bianalytic capacities and Calderon commutators

  • Maxim Ya MazalovEmail author
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Abstract

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.

Keywords

Singular integrals Calderon commutators Carleson measures Lipschitz graphs Littlewood–Paley theory Capacities Semiadditivity property Bianalytic functions Uniform approximation 

Notes

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Conflict of interest

There is no conflicts of interests.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Moscow Power Engineering Institute (National Research University), Smolensk BranchSmolenskRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia

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