|
Maximal operators of tree martingale transforms and their maximal operator inequalities
Author(s):
Tong-jun
He;
Yi
Shen
Journal:
Trans. Amer. Math. Soc.
360
(2008),
6595-6609.
MSC (2000):
Primary 60G46, 46B09
Posted:
July 28, 2008
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we define maximal operators for tree martingale transforms in  spaces and prove inequalities for them by using the  property.
References:
-
- 1.
- A. Benedek and R. Panzone, The spaces
 with mixed norm, Duke Math. J. 28(1961), 301-324. MR 23:A3451 - 2.
- J. Bourgain, Some remarks on Banach spaces in which martingale difference sequences are unconditional, Ark. Math. 21(1983), 163-168. MR 85a:46011
- 3.
- D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37(1966), 1494-1504. MR 34:8456
- 4.
- D. L. Burkholder, A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional, Ann. Prob. 9(1981), 997-1011. MR 83f:60070
- 5.
- D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Prob. 12(1984), 647-702. MR 86b:60080
- 6.
- S. Fridli and F. Schipp, Tree-martingales, Proc. 5th Pannonian Symp. on Math. Stat., Visegrád, Hungary(1985), 53-63. MR 89j:60064
- 7.
- J. Gosselin, Almost everywhere convergence of Vilenkin-Fourier series, Trans. Amer. Math. Soc. 185(1973), 345-370. MR 50:5369
- 8.
- T. J. He and Y. L. Hou, Some inequalities for tree martingales, Acta Mathematicae Applicatae Sinica (English Series) Vol. 21, No. 4(2005), 671-682. MR 2006h:60074
- 9.
- T. J. He , Y. X. Xiao and Y. L. Hou, Inequalities for vector-valued tree martingales, Proceeding of International Conference on Functional Space Theory and Its Applications, London, Research Information Ltd UK, 2004, 67-75.
- 10.
- T. J. He, Y. L. Hou and Y. Shen, Vector-valued tree martingales and some inequalities for vector-valued tree martingales, Acta Mathematica Hungarica (submitted to).
- 11.
- R. L. Long and P. D. Liu, Real interpolation of B-valued regular Martingale spaces, Chinese Annals of Mathematics 14A: 2(1993), 152-158. (in Chinese) MR 94j:60088
- 12.
- F. Schipp, Pointwise convergence of expansions with respect to certain product systems, Anal. Math. 2(1976), 65-76. MR 54:3281
- 13.
- F. Schipp, Universal contractive projections and a.e. convergence. Probability Theory and Applications, Essays to the Memory of József Mogyoródi. Eds.: J. Galambos, I. Kátai. Kluwer Academic Publishers, Dordrecht, Boston, London, 1992, 47-75. MR 95c:42040
- 14.
- E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, New Jersey, 1971. MR 46:4102
- 15.
- F. Weisz, Martingale Hardy spaces and their applications in Fourier analysis, Lecture Notes in Mathematics, Vol. 1568, Springer, Berlin, 1994. MR 96m:60108
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
60G46, 46B09
Retrieve articles in all Journals with MSC
(2000):
60G46, 46B09
Additional Information:
Tong-jun
He
Affiliation:
Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
Address at time of publication:
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, People's Republic of China
Email:
hetongjun@fzu.edu.cn
Yi
Shen
Affiliation:
Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
Email:
lhfu@hust.edu.cn
DOI:
10.1090/S0002-9947-08-04502-9
PII:
S 0002-9947(08)04502-9
Keywords:
Tree martingale,
$UMD$ spaces,
maximal operator
Received by editor(s):
August 28, 2006
Received by editor(s) in revised form:
March 1, 2007
Posted:
July 28, 2008
Additional Notes:
The authors were partially supported by NSFC Grant: 60574025
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org