Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Near-symmetry in $ A_\infty$ and refined Jones factorization

Author(s): Winston Ou
Journal: Proc. Amer. Math. Soc. 136 (2008), 3239-3245.
MSC (2000): Primary 42B25
Posted: May 6, 2008
MathSciNet review: 2407089
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We use variants of the Hardy-Littlewood maximal and the Cruz-Uribe-Neugebauer minimal operators to give direct characterizations of $ A_1$ and $ RH_\infty$ that clarify their near symmetry and yield elementary proofs of various known results, including Cruz-Uribe and Neugebauer's refinement of the Jones factorization theorem.

References:

1.
C. Bennett, Another characterization of BLO, Proceedings of the American Mathematical Society, 85, no. 4 (1982), pp. 552-556. MR 660603 (84h:42029)

2.
R. Coifman and R. Rochberg, Another characterization of BMO, Proceedings of the American Mathematical Society, 79 (1980), 249-254. MR 565349 (81b:42067)

3.
D. Cruz-Uribe and C. J. Neugebauer, The structure of the reverse Hölder classes, vol. 347, Transactions of the American Mathematical Society, 8 (1995), 2941-2960. MR 1308005 (95m:42026)

4.
J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies, vol. 116, North-Holland, Amsterdam, 1985. MR 807149 (87d:42023)

5.
R. Johnson, Changes of variable and $ A_p$ weights, Harmonic Analysis and Partial Differential Equations, Contemporary Mathematics, vol. 107, American Mathematical Society, Providence, RI, 1990, pp. 93-99. MR 1066472 (91f:42017)

6.
R. Johnson and C. J. Neugebauer, Homeomorphisms preserving ($ A_p$), Revista Matematica Iberoamericana, 3 (1987), 249-273. MR 990859 (90d:42013)

7.
R. Johnson and C. J. Neugebauer, Change of variable results for $ (A_p)$ and reverse Hölder $ RH_r$-classes, Transactions of the American Mathematical Society, 328 (1991), 639-666. MR 1018575 (92c:42019)

8.
P. W. Jones, Factorization of $ A_p$ weights, Annals of Mathematics, 111 (1980), 511-530. MR 577135 (82b:46035)

9.
B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Transactions of the American Mathematical Society, 165 (1972), 207-226. MR 0293384 (45:2461)

10.
W. Ou, The natural maximal operator on BMO, Proceedings of the American Mathematical Society, 129 (2001), 2919-2921. MR 1840094 (2003c:42022)

11.
J. O. Strömberg and R. L. Wheeden, Fractional integrals on weighted $ H^p$ and $ L^p$ spaces, Transactions of the American Mathematical Society, 287 (1985), 293-321. MR 766221 (86f:42016)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B25

Retrieve articles in all Journals with MSC (2000): 42B25

Additional Information:

Winston Ou
Affiliation: Department of Mathematics, Scripps College, Claremont, California 91711
Email: wcwou@scrippscollege.edu

DOI: 10.1090/S0002-9939-08-09459-8
PII: S 0002-9939(08)09459-8
Keywords: Minimal operator, natural extremal operators, BMO, $A_\infty $ weights.
Received by editor(s): August 7, 2007
Posted: May 6, 2008
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia