On some equivalent definitions of $\rho$- Carleson measures on the unit ball

Benoit F. Sehba

On some equivalent definitions of $\rho$- Carleson measures on the unit ball

Classical Analysis and ODEs 2016-03-01 v3 Complex Variables

Authors: Benoit F. Sehba

Abstract

We give in this paper some equivalent definitions of the so called $\rho$ -Carleson measures when $\rho(t)=(\log(4/t))^p(\log\log(e^4/t))^q$ , $0\le p,q<\infty$ . As applications, we characterize the pointwise multipliers on $LMOA(\mathbb S^n)$ and from this space to $BMOA(\mathbb S^n)$ . Boundedness of the Ces\`aro type integral operators on $LMOA(\mathbb S^n)$ and from $LMOA(\mathbb S^n)$ to $BMOA(\mathbb S^n)$ is considered as well.

Keywords

$\rho$-Carleson measures unit ball pointwise multipliers $LMOA(\mathbb S^n)$ $BMOA(\mathbb S^n)$ Ces\`aro type integral operators

Cite

@article{arxiv.0805.4448,
  title  = {On some equivalent definitions of $\rho$- Carleson measures on the unit ball},
  author = {Benoit F. Sehba},
  journal= {arXiv preprint arXiv:0805.4448},
  year   = {2016}
}

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23 pages

On some equivalent definitions of $\rho$- Carleson measures on the unit ball

Abstract

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