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)

     

On a Negative Result Concerning Interpolation with Change of Measures for Lorentz Spaces

Author(s): Elida V. Ferreyra
Journal: Proc. Amer. Math. Soc. 125 (1997), 1413-1417.
MSC (1991): Primary 46B70; Secondary 46E30
MathSciNet review: 1363418
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: In this note we show that the Stein-Weiss theorem on $L^p$ interpolation with change of measures cannot be extended to Lorentz spaces $L^{p,s}.$

References:

[B-S]
C. Bennett and R. Sharpley, Interpolation of operators, Pure and Applied Math. 129, Academic Press, 1988. MR 89e:46001

[C-H-K]
H.M. Chung, R.A. Hunt and D.S. Kurtz, The Hardy-Littlewood maximal function on $L(p,q)$ spaces with weights, Indiana Univ. Math. J. 31 (1982), 109-120. MR 83b:42021

[F]
E. Ferreyra, Ph.D. Thesis, FAMAF, Univ. Nac. de Córdoba, Córdoba, 1990.

[M-W]
B. Muckenhoupt and R.L. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261-274. MR 49:5275

[O]
E. Oklander, Interpolación, espacios de Lorentz y teorema de Marcinkiewicz, Cursos y seminarios de matemática, Univ. de Buenos Aires, fasc. 20 (1965). MR 36:680

[Sa]
E. Sawyer, Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator, Trans. Amer. Math. Soc. 281 (1984), 329-337. MR 85f:26013

[S-W1]
E.M. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159-172. MR 19:1184d

[S-W2]
E.M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, 1971. MR 46:4102

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46B70, 46E30

Retrieve articles in all Journals with MSC (1991): 46B70, 46E30

Additional Information:

Elida V. Ferreyra
Affiliation: Fa.M.A.F., Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 - Córdoba, Argentina
Email: eferrey@mate.uncor.edu

DOI: 10.1090/S0002-9939-97-03699-X
PII: S 0002-9939(97)03699-X
Keywords: Interpolation, Lorentz spaces
Received by editor(s): May 25, 1995
Received by editor(s) in revised form: November 16, 1995
Additional Notes: Partially supported by CONICET, CONICOR, SECYT (UNC), Argentina.
Communicated by: J. Marshall Ash
Copyright of article: Copyright 1997, American Mathematical Society




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