多复变的解析Besov空间上的Toeplitz算子(英文)

Toeplitz operators on analytic Besov spaces of several complex variables

将刻画由复测度μ诱导出的Toeplitz算子Tμ作用在单位球的解析Besov空间上是有界或紧的.对1<p<∞,α>-1,μ是n上的复测度,Toeplitz算子Tαμ作用到Bp上是有界的当且仅当测度|Pα,n+1(μ)(z)|p(1-|z|2)p(n+1-α)dυ(z)是一个(Bp,p)-Carleson测度.在同样的条件下,Toeplitz算子Tμα作用到Bp上是紧的当且仅当测度|Pα,n+1(μ)(z)|p(1-|z|2)p(n+1-α)dυ(z)是一个消失的(Bp,p)-Carleson测度.

In this note,we characterize complex measures μ on the unit ball for which the Toeplitz operator T is hounded or compact on the analytic Besov spaces Bpwith 1 ≤p 〈 ∞. We let 1 〈p 〈 ∞ , let α 〉-1, and let μ be the complex measure. The Toeplitz operator Tμ is hounded on Bp if and only if the measure ）-Carleson measure. In the same conditions, the Toeplitz operator Tμ is compact on Bp if and only if the measure s a vanishing（Bp ,p）-Carleson measure.