Hostname: page-component-669899f699-swprf Total loading time: 0 Render date: 2025-04-28T15:38:17.726Z Has data issue: false hasContentIssue false
  • English
  • Français

On some convexity questions of Handelman

Part of: Harmonic analysis in several variables Real functions

Published online by Cambridge University Press:  16 May 2024

Brian Simanek Open the ORCID record for Brian Simanek [Opens in a new window]
Brian Simanek*
Affiliation:
Department of Mathematics, Baylor University, Waco, TX 76706, United States
*
e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We resolve some questions posed by Handelman in 1996 concerning log convex $L^1$ functions. In particular, we give a negative answer to a question he posed concerning the integrability of $h^2(x)/h(2x)$ when h is $L^1$ and log convex and $h(n)^{1/n}\rightarrow 1$.

Keywords

Log convex functionsConvexityIntegrable functions

MSC classification

Primary: 26A51: Convexity, generalizations
Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 4 , December 2024 , pp. 936 - 939
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Handelman, D., Eventual positivity for analytic functions . Math. Ann. 304(1996), no. 2, 315–338.CrossRefGoogle Scholar
Simon, B., Convexity: An analytic viewpoint, Cambridge Tracts in Mathematics, 187, Cambridge University Press, Cambridge, 2011.CrossRefGoogle Scholar