Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Characterizations of bounded mean oscillation


Author: Stephen Jay Berman
Journal: Proc. Amer. Math. Soc. 51 (1975), 117-122
MSC: Primary 42A92; Secondary 46E30
MathSciNet review: 0374805
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Recall that an integrable function $ f$ on a cube $ {Q_0}$ in $ {{\mathbf{R}}^n}$ is said to be of bounded mean oscillation if there is a constant $ K$ such that for every parallel subcube $ Q$ of $ {Q_0}$ there exists a constant $ {a_Q}$ such that $ \int_Q {\vert f - {a_Q}\vert \leq K\vert Q\vert} $, where $ \vert Q\vert$ denotes the volume of $ Q$. We prove here that if there is an integer $ d$ and a constant $ K$ such that for every parallel subcube $ Q$ of $ {Q_0}$ there exists a polynomial $ {p_Q}$ of degree $ \leq d$ such that $ \int_Q {\vert f - {p_Q}\vert \leq K\vert Q\vert} $, then $ f$ is of bounded mean oscillation.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A92, 46E30

Retrieve articles in all journals with MSC: 42A92, 46E30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0374805-5
PII: S 0002-9939(1975)0374805-5
Keywords: Bounded mean oscillation, polynomial approximation
Article copyright: © Copyright 1975 American Mathematical Society