The AMS website will be down for maintenance on May 23 between 6:00am - 8:00am EDT. For questions please contact AMS Customer Service at or (800) 321-4267 (U.S. & Canada), (401) 455-4000 (Worldwide).


Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A remark on the maximal operator for radial measures

Author: Adrián Infante
Journal: Proc. Amer. Math. Soc. 139 (2011), 2899-2902
MSC (2000): Primary 42B25
Published electronically: January 14, 2011
MathSciNet review: 2801630
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to prove that there exist measures $ d\mu(x)=\gamma(x)dx$, with $ \gamma(x)=\gamma_{0}(\vert x\vert)$ and $ \gamma_{0}$ being a decreasing and positive function, such that the Hardy-Littlewood maximal operator, $ \mathcal{M}_{\mu}$, associated to the measure $ \mu$ does not map $ L^{p}_{\mu}(\mathbb{R}^{n})$ into weak $ L^{p}_{\mu}(\mathbb{R}^{n})$, for every $ p<\infty$. This result answers an open question of P. Sjögren and F. Soria.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B25

Retrieve articles in all journals with MSC (2000): 42B25

Additional Information

Adrián Infante
Affiliation: Department of Mathematics, Universidad Simón Bolívar, Caracas, Venezuela

Keywords: Rotation invariant measure, maximal operator, is of weak type
Received by editor(s): April 6, 2010
Received by editor(s) in revised form: August 4, 2010
Published electronically: January 14, 2011
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2011 American Mathematical Society

American Mathematical Society