On functions in \(p\)-adic \(BMO\) and the distribution of prime integers
type: Item
instance of: scholarly article
title: On functions in \(p\)-adic \(BMO\) and the distribution of prime integers
zbMATH Open document ID: 1119.46029
author: Steven G. Krantz
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-02-14T00:00:00Z
review text: The author investigates the relationship between the classical BMO space on the real line, with a norm \[ \| f\| _*=\sup _{I}\frac{1}{| I|}\int_I | f(x)-f_I(x)|\,dx,\; f_I=\frac{1}{| I|}\int_I| f(x)|\,dx,\tag{*} \] where \(I\) is an interval, and the \(p\)-adic BMO space, denoted by \(\text{BMO}_p\), with the norm \(\| f\| _{*,p}\) given by \((*)\), but now the supremum is taken over all intervals of the form \((m+\frac{j-1}{p^k}, m+\frac{j}{p^k})\), where \(m\) is an integer, \(1\leq j\leq p^k\), and \(p\) a positive prime integer, \(k=1,2,\dots\). In particular, it is proved that \(\bigcap_{p}\text{BMO}_p\neq\text{BMO}\) and a relation to the distribution of primes is given.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 11N05
zbMATH DE Number: 5125984
zbMATH Keywords: \(p\)-adic bounded mean oscillation space
zbMATH Keywords: distribution of primes
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.03.058
OpenAlex ID: W2041778006
cites work: Q3217388
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DOI: 10.1016/J.JMAA.2006.03.058
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description: scientific article; zbMATH DE number 5125984