期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2009
卷号：2009
DOI：10.1155/2009/921324
出版社：Hindawi Publishing Corporation
摘要：We have shown that if the Toeplitz operator 𝑇𝜙 on the
Bergman space 𝐿2𝑎(𝔻) belongs to the Schatten class 𝑆𝑝,1≤𝑝<∞, then 𝜙∈𝐿𝑝(𝔻,𝑑𝜆), where 𝜙 is the Berezin transform of 𝜙,𝑑𝜆(𝑧)=𝑑𝐴(𝑧)/(1−|𝑧|2)2, and 𝑑𝐴(𝑧) is the normalized area measure on the open unit disk 𝔻. Further, if 𝜙∈𝐿𝑝(𝔻,𝑑𝜆) then 𝜙∈𝐿𝑝(𝔻,𝑑𝜆) and 𝑇𝜙∈𝑆𝑝. For certain
subclasses of 𝐿∞(𝔻), necessary and sufficient conditions characterizing
Schatten class Toeplitz operators are also obtained.
