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Bianalytic capacities and Calderon commutators

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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.

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  1. Moscow Power Engineering Institute (National Research University), Smolensk Branch, Smolensk, Russia

    Maxim Ya Mazalov

  2. St. Petersburg State University, St. Petersburg, Russia

    Maxim Ya Mazalov

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  1. Maxim Ya Mazalov
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Correspondence to Maxim Ya Mazalov.

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This work is supported by the Russian Science Foundation under Grant 17-11-01064.

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Mazalov, M.Y. Bianalytic capacities and Calderon commutators. Anal.Math.Phys. 9, 1099–1113 (2019). https://doi.org/10.1007/s13324-018-0276-y

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  • DOI: https://doi.org/10.1007/s13324-018-0276-y

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