English

Carleson measures for Hardy and Bergman spaces in the quaternionic unit ball

Complex Variables 2017-01-25 v2

Abstract

We study a characterization of slice Carleson measures and of Carleson measures for the both the Hardy spaces Hp(B)H^p(\mathbb B) and the Bergman spaces Ap(B)\mathcal A^p(\mathbb B) of the quaternionic unit ball B\mathbb B. In the case of Bergman spaces, the characterization is done in terms of the axially symmetric completion of a pseudohyperbolic disc in a complex plane. We also show that a characterization in terms of pseudohyperbolic balls is not possible.

Keywords

Cite

@article{arxiv.1601.03031,
  title  = {Carleson measures for Hardy and Bergman spaces in the quaternionic unit ball},
  author = {Irene Sabadini and Alberto Saracco},
  journal= {arXiv preprint arXiv:1601.03031},
  year   = {2017}
}

Comments

Version to appear on J. London Math. Soc. (accepted), 21 pages, 1 figure