广州大学学报(自然科学版)
廣州大學學報(自然科學版)
엄주대학학보(자연과학판)
JOURNAL OF GUANGZHOU UNIVERSITY(NATURAL SCIENCE EDITION)
2010年
4期
6-9
,共4页
Toeplitz算子%解析%Besov空间
Toeplitz算子%解析%Besov空間
Toeplitz산자%해석%Besov공간
Toeplitz operator%analytic%Besov spaces
将刻画由复测度μ诱导出的Toeplitz算子Tμ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Bn上的复测度,Toeplitz算子Tμα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)dv(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)dv(z)是一个消失的(Bp,p)-Carleson测度.
將刻畫由複測度μ誘導齣的Toeplitz算子Tμ用在單位毬的解析Besov空間上是有界或緊的.對1<p<∞,α>-1,μ是Bn上的複測度,Toeplitz算子Tμα作用到Bp上是有界的噹且僅噹測度| Pα,n+1(μ)(z)|p(1-|z|2)p(n+1-α)dv(z)是一箇(Bp,p)-Carleson測度.在同樣的條件下,Toeplitz算子Tμα作用到Bp上是緊的噹且僅噹測度|Pα,n+1(μ)(z)|p(1-|z|2)p(n+1-α)dv(z)是一箇消失的(Bp,p)-Carleson測度.
장각화유복측도μ유도출적Toeplitz산자Tμ용재단위구적해석Besov공간상시유계혹긴적.대1<p<∞,α>-1,μ시Bn상적복측도,Toeplitz산자Tμα작용도Bp상시유계적당차부당측도| Pα,n+1(μ)(z)|p(1-|z|2)p(n+1-α)dv(z)시일개(Bp,p)-Carleson측도.재동양적조건하,Toeplitz산자Tμα작용도Bp상시긴적당차부당측도|Pα,n+1(μ)(z)|p(1-|z|2)p(n+1-α)dv(z)시일개소실적(Bp,p)-Carleson측도.
In this note,we characterize complex measures μ on the unit ball for which the Toeplitz operator Tμ is bounded 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 Tμα is bounded on Bp if and only if the measure | Pα,n+1(μ)(z)|p(1-|z|2)p(n+1-α)dv(z)is a (Bp ,p)-Carleson measure. In the same conditions, the Toeplitz operator Tμα is compact on Bp if and only if the measure |Pα,n+1(μ)(z)|p(1-|z|2)p(n+1-α)dv(z)is a vanishing(Bp ,p)-Carleson measure.