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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we show that the 
-th order variation operator, for both the Fejér and Poisson kernels, are bounded from 
to 
, 
, when 
. Counterexamples are given if 
.
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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
