2 results
LIPSCHITZ SPACES AND BOUNDED MEAN OSCILLATION OF HARMONIC MAPPINGS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 88 / Issue 1 / August 2013
- Published online by Cambridge University Press:
- 18 January 2013, pp. 143-157
- Print publication:
- August 2013
-
- Article
-
- You have access
- Export citation
-
We first study the bounded mean oscillation of planar harmonic mappings. Then we establish a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings. Finally, we obtain sharp estimates on the Lipschitz number of planar harmonic mappings in terms of the bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to
$BM{O}_{2} $ as a Banach space.
Subspaces of de Branges Spaces Generated by Majorants
-
- Journal:
- Canadian Journal of Mathematics / Volume 61 / Issue 3 / 01 June 2009
- Published online by Cambridge University Press:
- 20 November 2018, pp. 503-517
- Print publication:
- 01 June 2009
-
- Article
-
- You have access
- Export citation
-
For a given de Branges space
$\mathcal{H}(E)$ we investigate de Branges subspaces defined in terms of majorants on the real axis. If 
$\omega $ is a nonnegative function on 
$\mathbb{R}$, we consider the subspace
$${{\mathcal{R}}_{\omega }}(E)=\text{Clo}{{\text{s}}_{\mathcal{H}(E)}}\{F\in \mathcal{H}(E):\text{there exists }C>0:|{{E}^{-1}}F|\le C\omega \,on\,\mathbb{R}\}.$$We show that
${{\mathcal{R}}_{\omega }}(E)$ is a de Branges subspace and describe all subspaces of this form. Moreover, we give a criterion for the existence of positive minimal majorants.
