On Riesz type inequalities for harmonic mappings on the unit disk

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.

arXiv comment37 pages

References in corpus (1)

• On some Riesz and Carleman type inequalities for harmonic functions on the unit disk

Cited by in corpus (1)

• Riesz-Fejér inequalities for harmonic functions