Citation
Holden, Peter James (1987) Extension Theorems for Functions of Vanishing Mean Oscillation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/f7k9-rh88. https://resolver.caltech.edu/CaltechTHESIS:11132015-131516478
Abstract
A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in Rd converges to zero with the volume of the cubes. We establish necessary and sufficient conditions for a locally integrable function defined on a bounded measurable set of positive measure to be the restriction to that set of a VMO function.
We consider the similar extension problem pertaining to BMO(ρ) functions; that is, those VMO functions whose mean oscillation over any cube is O (ρ(ℓ(Q))) where ℓ(Q) is the length of Q and ρ is a positive, non-decreasing function with ρ(0+) = 0.
We apply these results to obtain sufficient conditions for a Blaschke sequence to be the zeros of an analytic BMO(ρ) function on the unit disc.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
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| Subject Keywords: | Mathematics |
| Degree Grantor: | California Institute of Technology |
| Division: | Physics, Mathematics and Astronomy |
| Major Option: | Mathematics |
| Thesis Availability: | Public (worldwide access) |
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| Thesis Committee: |
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| Defense Date: | 14 May 1987 |
| Record Number: | CaltechTHESIS:11132015-131516478 |
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:11132015-131516478 |
| DOI: | 10.7907/f7k9-rh88 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 9279 |
| Collection: | CaltechTHESIS |
| Deposited By: | Benjamin Perez |
| Deposited On: | 13 Nov 2015 22:06 |
| Last Modified: | 16 Apr 2021 22:18 |
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