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

Author(s): Parthena Avramidou
Journal: Proc. Amer. Math. Soc. 133 (2005), 175-184.
MSC (2000): Primary 28A15, 42A85; Secondary 43A15
Posted: July 26, 2004
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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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3.: A. Nagel and E. M. Stein, On certain maximal functions and approach regions, Advances in Mathematics 54 (1984), 83-106. MR 86a:42026
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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: 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
Posted: July 26, 2004
Communicated by: Andreas Seeger
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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