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On Ahlfors–Beurling Operator


We investigate regularity properties of solutions of Beltrami equation expressed in terms of moduli of continuity. In particular, we prove that a class of Calderon–Zygmund operators, including Ahlfors–Beurling operator, preserves certain type of modulus of continuity of compactly supported functions. We also prove a purely topological result which easily gives injectivity of normal solutions of Beltrami equation.

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Correspondence to Miloš Arsenović.

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Dedicated to 80th anniversary of Professor Vladimir Gutlyanskii

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 18, No. 3, pp. 292–302, July–September, 2021.

This investigation was supported Supported by Ministry of Science, Serbia, project OI 174017 and project OI 174032.

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Arsenović, M., Mateljević, M. On Ahlfors–Beurling Operator. J Math Sci 259, 1–9 (2021).

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  • Beltrami equation
  • Ahlfors–Beurlling operator
  • weakly closed forms