A Caltech Library Service

Extension Theorems for Functions of Vanishing Mean Oscillation


Holden, Peter James (1987) Extension Theorems for Functions of Vanishing Mean Oscillation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/f7k9-rh88.


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.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Goddard, William A., III (advisor)
  • Wolff, Thomas H. (co-advisor)
Thesis Committee:
  • Goddard, William A., III (chair)
  • Beauchamp, Jesse L.
  • Grubbs, Robert H.
  • Bercaw, John E.
  • Wolff, Thomas H.
Defense Date:14 May 1987
Record Number:CaltechTHESIS:11132015-131516478
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9279
Deposited By: Benjamin Perez
Deposited On:13 Nov 2015 22:06
Last Modified:16 Apr 2021 22:18

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page