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Variation inequalities for the Fejér and Poisson kernels
Author(s):
Roger
L.
Jones;
Gang
Wang
Journal:
Trans. Amer. Math. Soc.
356
(2004),
4493-4518.
MSC (2000):
Primary 42A24;
Secondary 26D05
Posted:
January 13, 2004
MathSciNet review:
2067131
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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  .
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
DOI:
10.1090/S0002-9947-04-03397-5
PII:
S 0002-9947(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
Posted:
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 of article:
Copyright
2004,
American Mathematical Society
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