### Abstract

We introduce a concept of joint Carleson measure and characterize when the difference of two composition operators on A_{α}
^{p}(B_{n}), the weighted Bergman space over the unit ball B_{n} in C^{n}, is bounded or compact. We apply this joint Carleson measure characterization to composition operators with smooth symbols and construct an interesting example which shows that the boundedness or the compactness depends on p when n ≥ 2. This is in sharp contrast with the single composition operator case where the boundedness or the compactness is independent of p>0. Moreover, the compact difference on the weighted Bergman spaces over the unit disc is known to be independent of p>0, and the compact difference on A_{α}
^{p}(B_{n}) is known to be independent of p>0 if each composition operator is bounded on A_{β}
^{p}(B^{n}) for some -1< β < α [2].

Original language | English |
---|---|

Pages (from-to) | 1119-1142 |

Number of pages | 24 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 419 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 Nov 15 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Joint Carleson measure and the difference of composition operators on A _{α}
^{p}(B_{n}).** / Koo, Hyung Woon; Wang, Maofa.

Research output: Contribution to journal › Article

_{α}

^{p}(B

_{n})',

*Journal of Mathematical Analysis and Applications*, vol. 419, no. 2, pp. 1119-1142. https://doi.org/10.1016/j.jmaa.2014.05.037

}

TY - JOUR

T1 - Joint Carleson measure and the difference of composition operators on Aα p(Bn)

AU - Koo, Hyung Woon

AU - Wang, Maofa

PY - 2014/11/15

Y1 - 2014/11/15

N2 - We introduce a concept of joint Carleson measure and characterize when the difference of two composition operators on Aα p(Bn), the weighted Bergman space over the unit ball Bn in Cn, is bounded or compact. We apply this joint Carleson measure characterization to composition operators with smooth symbols and construct an interesting example which shows that the boundedness or the compactness depends on p when n ≥ 2. This is in sharp contrast with the single composition operator case where the boundedness or the compactness is independent of p>0. Moreover, the compact difference on the weighted Bergman spaces over the unit disc is known to be independent of p>0, and the compact difference on Aα p(Bn) is known to be independent of p>0 if each composition operator is bounded on Aβ p(Bn) for some -1< β < α [2].

AB - We introduce a concept of joint Carleson measure and characterize when the difference of two composition operators on Aα p(Bn), the weighted Bergman space over the unit ball Bn in Cn, is bounded or compact. We apply this joint Carleson measure characterization to composition operators with smooth symbols and construct an interesting example which shows that the boundedness or the compactness depends on p when n ≥ 2. This is in sharp contrast with the single composition operator case where the boundedness or the compactness is independent of p>0. Moreover, the compact difference on the weighted Bergman spaces over the unit disc is known to be independent of p>0, and the compact difference on Aα p(Bn) is known to be independent of p>0 if each composition operator is bounded on Aβ p(Bn) for some -1< β < α [2].

KW - Boundedness

KW - Carleson measure

KW - Compactness

KW - Difference of composition operators

KW - Unit ball

UR - http://www.scopus.com/inward/record.url?scp=84903447401&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903447401&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2014.05.037

DO - 10.1016/j.jmaa.2014.05.037

M3 - Article

VL - 419

SP - 1119

EP - 1142

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -