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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Variation inequalities for the Fejér and Poisson kernels


Authors: Roger L. Jones and Gang Wang
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 4493-4518
MSC (2000): Primary 42A24; Secondary 26D05
DOI: https://doi.org/10.1090/S0002-9947-04-03397-5
Published electronically: January 13, 2004
MathSciNet review: 2067131
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Abstract: In this paper we show that the $\varrho$-th order variation operator, for both the Fejér and Poisson kernels, are bounded from $L^p$ to $L^p$, $1<p<\infty$, when $\varrho >2$. Counterexamples are given if $\varrho =2$.


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Additional Information

Roger L. Jones
Affiliation: Department of Mathematics, DePaul University, 2320 N. Kenmore, Chicago, Illinois 60614
Email: rjones@condor.depaul.edu

Gang Wang
Affiliation: Department of Mathematics, DePaul University, 2320 N. Kenmore, Chicago, Illinois 60614
Email: gwang@condor.depaul.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03397-5
Keywords: Fej\'er kernel, Poisson kernel, square functions, variation, jump inequalities
Received by editor(s): August 17, 2001
Received by editor(s) in revised form: May 13, 2003
Published electronically: January 13, 2004
Additional Notes: The first aurthor was partially supported by a grant from the DePaul University Liberal Art and Science research program
The second author was partially supported by NSF grant DMS-0071759
Article copyright: © Copyright 2004 American Mathematical Society