Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419175 | Journal of Mathematical Analysis and Applications | 2013 | 8 Pages |
Abstract
If f and g are analytic functions in the unit disc D we define Sg(f)(z)=â«0zfâ²(w)g(w)dw,(zâD). If g is bounded then the integral operator Sg is bounded on the Bloch space, on the Dirichlet space, and on BMOA. We show that Sg is norm-attaining on the Bloch space and on BMOA for any bounded analytic function g, but does not attain its norm on the Dirichlet space for non-constant g. Some results are also obtained for Sg on the little Bloch space, and for another integral operator Tg from the Dirichlet space to the Bergman space.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Junming Liu, Chengji Xiong,