一类不变的Hankel算子(英文)

A Kind of Invariant Hankel Operators

英文关键词:weighted Bergman space  Casimir operator  invariant Hankel operator  'periodic' paracommutator  Schatten-von Neumann class.

中文摘要:

      对于Ｌ^a,2（Ｄ）的两类Ｍｏｅｂｉｕｓ不变子空间Ａ_l^a,2（Ｄ）与Ａ_l^-a,2（Ｄ），定义了对解析的记号函数ｂ（ｚ）的大的和小的Ｈａｎｋｅｌ算子Ｈ_b^ll′与ｈ_b^ll′，研究了它们的有界性、紧性及其Ｓｃｈａｔｔｅｎ－ｖｏｎ Ｎｅｕｍａｎｎ类的Ｓ_P估计．性质。

英文摘要:

      For two kinds of the Moebius invariant subspace A_l^a,2(D) and A_l^-a,2(D) of L^a,2(D), we define big and small Hankel operators H_b^ll′ and h_b^ll′ for the analytic symbol function b(z), and study their boundedness, compactness and Schatten-von Neumanu classes S_p-estimates, and hence develope Schatten -von Neumann properties of these op- erators.