Sharp estimates for holomorphic functions on the unit ball of ℂⁿ

Abstract

The purpose of the paper is to establish sharp estimates for the Hilbert transform and the Riesz projection on the unit sphere of . The proof rests on the existence of certain superharmonic functions on satisfying appropriate majorization conditions.

Keywords:

• harmonic function
• holomorphic function
• Riesz projection
• Hilbert transform
• best constants

AMS Subject Classifications:

• 42B35
• 32A10
• 42A50
• 32A50

Acknowledgements

The author would like to thank the editors and an anonymous referee for the careful reading of the first version of the manuscript.

Additional information

Funding

The research was partially supported by the Narodowe Centrum Nauki (National Science Centre) grant DEC-2012/05/B/ST1/00412.