On Riesz type inequalities for harmonic mappings on the unit disk

Kalaj, David

doi:10.1090/tran/7808

On Riesz type inequalities for harmonic mappings on the unit disk
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Trans. Amer. Math. Soc. 372 (2019), 4031-4051 Request permission

Abstract:

We prove some sharp inequalities for complex harmonic functions on the unit disk. The results extend a M. Riesz conjugate function theorem and some well-known estimates for holomorphic functions. We apply some of results to the isoperimetric inequality for harmonic mappings.

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