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Subordination of planar harmonic functions. (English) Zbl 1020.30021

Summary: We initiate a systematic study of subordination of harmonic functions. We establish results about coefficient relationships, integral means, and majorization of the Jacobian. In connection with the last result, we use affine and linear invariant families of harmonic functions to obtain the surprising result that the radius of majorization of the Jacobian for harmonic functions coincides with the same quantity for analytic functions.

MSC:

30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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