### 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 |
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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