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)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts

Author(s): María C. Pereyra; Lesley A. Ward
Journal: Proc. Amer. Math. Soc. 126 (1998), 135-144.
MSC (1991): Primary 42B99; Secondary 47A10
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We analyze the stability of Muckenhoupt's $\bold{ RH} ^d_p$ and $\bold{ A} _p^d$ classes of weights under a nonlinear operation, the $\lambda $-operation. We prove that the dyadic doubling reverse Hölder classes $\bold{ RH} ^d_p$ are not preserved under the $\lambda $-operation, but the dyadic doubling $A_p$ classes $\bold{ A} _p^d$ are preserved for $0\leq \lambda \leq 1$. We give an application to the structure of resolvent sets of dyadic paraproduct operators.

References:

[B]
S. Buckley, Summation conditions on weights. Michigan Math. J. 40 #1, 153-170 (1993). MR 94d:42021

[Ch]
M. Christ, Lectures on singular integral operators. Regional Conference Series in Math, AMS # 77 (1990). MR 92f:42021

[D]
G. David, Wavelets and singular integrals on curves and surfaces. Springer Verlag Lecture Notes in Math. # 1465 (1991). MR 92k:42021

[FKP]
R. Fefferman, C. Kenig, J. Pipher, The theory of weights and the Dirichlet problem for elliptic equations. Annals of Math. # 134, 65-124 (1991). MR 93h:31010

[GC-RF]
J. Garcia-Cuerva, J.L. Rubio de Francia, Weighted norm inequalities and related topics. North Holland (1985). MR 87d:42023

[H]
A. Haar, Zur Theorie der orthogonalen Funktionensysteme. Math. Ann. # 69, 331-371 (1910).

[JN]
R. Johnson, C. J. Neugebauer, Homeomorphisms preserving $\bold{ A} _p^d$. Revista Matemática Iberoamericana Vol. 3, No. 2, 249-273 (1987). MR 90d:42013

[M]
Y. Meyer, Ondelettes et Opérateurs II. Herman (1990). MR 93i:42003

[P1]
M. C. Pereyra, On the resolvents of dyadic paraproducts. Revista Matemática Iberoamericana Vol. 10 No. 3, 627-664 (1994). MR 96e:42021

[P2]
M. C. Pereyra, On the resolvent of the dyadic paraproduct, and a nonlinear operation on $RH_p$ weights. Cont. Math. of AMS. Vol 189, 461-471 (1995). MR 96h:42016

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42B99, 47A10

Retrieve articles in all Journals with MSC (1991): 42B99, 47A10

Additional Information:

María C. Pereyra
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-1141
Email: crisp@math.unm.edu

Lesley A. Ward
Affiliation: Department of Mathematics, Harvey Mudd College, Claremont, California 91711
Email: lesley@math.rice.edu

DOI: 10.1090/S0002-9939-98-04400-1
PII: S 0002-9939(98)04400-1
Keywords: Muckenhoupt weights, reverse H\"older $RH_p$, $A_p$, doubling weights, dyadic paraproducts, paraexponentials
Received by editor(s): May 9, 1996
Additional Notes: This research was supported in part by (CP) NSF grant #DMS-93-04580 and (LW) at MSRI by NSF grant #DMS-90-22140.
Communicated by: J. Marshall Ash
Copyright of article: Copyright 1998, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google