Growth description of pth means of the Green potential in the unit ball

Abstract

We describe the growth of pth means, , of the invariant Green potential in the unit ball in in terms of smoothness properties of a measure. In particular, a criterion of boundedness of pth means of the potential is obtained, a result of M. Stoll is generalized.

Keywords:

• Green potential
• unit ball
• invariant Laplacian
• -subharmonic function
• Riesz measure

AMS Subject Classifications:

• 31B25
• 31C05

Acknowledgements

The authors thank the anonymous referee for helpful comments.

Notes

No potential conflict of interest was reported by the authors.