Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

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
MathSciNet review: 2085167
Retrieve article in: PDF
This article is available free of charge

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.

References:

1.: A. Bellow, Perturbation of a Sequence, Advances in Mathematics 78 (1989), 131-139. MR 91f:28009
2.: W. Emerson, The pointwise ergodic theorem for amenable groups, Amer. J. Math. 96 (1974), 472-487. MR 50:7403
3.: A. Nagel and E. M. Stein, On certain maximal functions and approach regions, Advances in Mathematics 54 (1984), 83-106. MR 86a:42026
4.: K. Reinhold-Larsson, Discrepancy of behavior of perturbed sequences in L spaces, Proc. Amer. Math. Soc. 120 (1994), 865-874. MR 94e:28008
5.: S. Sawyer, Maximal inequalities of weak type, Ann. of Math. (2) 84 (1966), 157-174. MR 35:763
6.: E. M. Stein, On limits of sequences of operators, Ann. of Math. (2) 74 (1961), 140-170. MR 23:A2695

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 28A15, 42A85, 43A15

Retrieve articles in all Journals with MSC (2000): 28A15, 42A85, 43A15

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.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|