Variation inequalities for the Fejér and Poisson kernels
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- by Roger L. Jones and Gang Wang PDF
- Trans. Amer. Math. Soc. 356 (2004), 4493-4518 Request permission
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 $\varrho =2$.References
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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
- 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 - © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2067131