Mathematical Research Letters

Volume 23 (2016)

Number 4

Commutators of singular integrals, the Bergman projection, and boundary regularity of elliptic equations in the plane

Pages: 1221 – 1246

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n4.a11

Author

Alexander Tumanov (Department of Mathematics, University of Illinois, Urbana, Il., U.S.A.)

Abstract

We obtain estimates of commutators of singular integral operators in Lipschitz spaces and apply the results to boundary regularity of elliptic equations in the plane. We obtain an explicit asymptotic formula for the Bergman projection.

Keywords

elliptic equation, commutator, singular integral, Bergman projection

2010 Mathematics Subject Classification

30H20, 35J56, 42B20

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