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Interpolation theorem on Lorentz spaces over weighted measure spaces
Authors:
Shinya Moritoh, Miyuki Niwa and Takuya Sobukawa
Journal:
Proc. Amer. Math. Soc. 134 (2006), 2329-2334
MSC (2000):
Primary 46B70; Secondary 46E30
Posted:
February 6, 2006
MathSciNet review:
2213706
Full-text PDF Free Access
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Abstract: In 1997 Ferreyra proved that it is impossible to extend the Stein-Weiss theorem in the context of Lorentz spaces. In this paper we obtain an interpolation theorem on Lorentz spaces over weighted measure spaces.
References
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 and  and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273-299. MR 0203444 (34:3295)
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E. V. Ferreyra, On a negative result concerning interpolation with change of measures for Lorentz spaces, Proc. Amer. Math. Soc. 125 (1997), 1413-1417. MR 1363418 (97i:46055)
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R. A. Hunt, On
 spaces, Enseign. Math. 12 (1966), 249-276. MR 0223874 (36:6921)
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M. Kubo (Niwa) and S. Moritoh, An approach to Marcinkiewicz type interpolation theorem on weighted Lorentz spaces, Annual Report of Graduate School of Human Culture, Nara Women's Univ. 16 (2000), 259-265.
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E. M. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159-172. MR 0092943 (19:1184d)
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Additional Information
Shinya Moritoh
Affiliation:
Department of Mathematics, Nara Women's University, Kitauoya-Nishimachi Nara, Japan 630-8506
Email:
moritoh@cc.nara-wu.ac.jp
Miyuki Niwa
Affiliation:
Graduate School of Human Culture, Nara Women's University, Kitauoya-Nishimachi Nara, Japan 630-8506
Email:
yam.kubo@cc.nara-wu.ac.jp
Takuya Sobukawa
Affiliation:
Department of Education, Okayama University, 3-1-1 Tsushima-Naka Okayama, Japan 700-8530
Email:
sobu@cc.okayama-u.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08395-X
PII:
S 0002-9939(06)08395-X
Keywords:
Weighted Lorentz spaces,
weighted interpolation
Received by editor(s):
January 10, 2003
Received by editor(s) in revised form:
March 8, 2005
Posted:
February 6, 2006
Communicated by:
Christopher D. Sogge
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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