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

 

Convolution operators induced by approximate identities and pointwise convergence in $L_p(\mathbb{R} )$ spaces


Author: Parthena Avramidou
Journal: Proc. Amer. Math. Soc. 133 (2005), 175-184
MSC (2000): Primary 28A15, 42A85; Secondary 43A15
Published electronically: July 26, 2004
MathSciNet review: 2085167
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Abstract | References | Similar Articles | Additional Information

Abstract: Given a sequence of kernels $\phi_n$ for which the operators $T_nf=\phi_n\ast f$ converge a.e. in all $L_p(\mathbb{R} )$ spaces, $p\geq 1$, a perturbation method is provided with the property that the modified convolution operators converge pointwise only in selective spaces.


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Additional Information

Parthena Avramidou
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Email: avramidou@math.ohio-state.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07494-5
PII: S 0002-9939(04)07494-5
Received by editor(s): August 6, 2003
Received by editor(s) in revised form: September 11, 2003
Published electronically: July 26, 2004
Communicated by: Andreas Seeger
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.