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

 

The convergence almost everywhere of Legendre series


Author: Harry Pollard
Journal: Proc. Amer. Math. Soc. 35 (1972), 442-444
MSC: Primary 33A45
MathSciNet review: 0302973
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Abstract: It is proved that the Legendre series of an $ {L^p}$ function converges almost everywhere, provided $ 4/3 < p < \infty $. The result fails if $ 1 \leqq p < 4/3$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0302973-7
PII: S 0002-9939(1972)0302973-7
Keywords: Legendre series, convergence almost everywhere, mean convergence, equiconvergence
Article copyright: © Copyright 1972 American Mathematical Society