Norm-attaining integral operators on analytic function spaces

Details Norm-attaining integral operators on analytic function spaces Norm-attaining integral operators on analytic function spaces

2012-03-22

arxiv.org/abs/1203.4904v1

Mathematics

Complex Variables

9 pages

Scientific paper

Any bounded analytic function $g$ induces a bounded integral operator $S_g$ on the Bloch space, the Dirichlet space and $BMOA$ respectively. $S_g$ attains its norm on the Bloch space and $BMOA$ for any $g$, but does not attain its norm on the Dirichlet space for non-constant $g$. Some results are also obtained for $S_g$ on the little Bloch space, and for another integral operator $T_g$ from the Dirichlet space to the Bergman space.

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