Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball

By Dana D. Clahane, S. Stević. 2006

82 citations recorded by the source corpus.

For, let and denote, respectively, the-Bloch and holomorphic-Lipschitz spaces of the open unit ball in. It is known that and are equal as sets when. We prove that these spaces are additionally norm-equivalent, thus extending known results for and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator from to.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bd7c4c03101f90649a4a90dc272a7e5403ffcc4d

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In Applied Mathematics

1. S. Stević
2. Songxiao Li
3. Stevo Stevi´c
4. Flavia Colonna
5. Robert F. Allen
6. Steven G. Krantz
7. Weifeng Yang
8. Dinggui Gu

In Geometry and Topology

1. S. Stević
2. Songxiao Li
3. Stevo Stevi´c
4. Lothar Berg

Citations in the corpus

• WEIGHTED COMPOSITION OPERATORS BETWEEN H∞ AND α-BLOCH SPACES IN THE UNIT BALL (2008, background): “Moreover, in [1] it was shown that the quantities ‖f‖Bα and |f(0)|+ aα(f) are equivalent.”
• Weighted Composition Operators between Mixed Norm Spaces and Spaces in the Unit Ball (2007, background): “Recall that the β-Bloch space β(B) = β is the space of all f ∈ H(B) such that ‖ f ‖ β = | f (0)|+ supz∈B(1−|z|(2))β| f (z)| <∞, where f (z)= ∑n j=1zj(∂ f /∂zj)(z) (see [6]), and the little β-Bloch space β 0(B) = β0 is the space of all f ∈ H(B) such that lim|z|→1(1−|z|2)| f (z)| = 0.”