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Interpolation theorem on Lorentz spaces over weighted measure spaces

Author(s): Shinya Moritoh; Miyuki Niwa; Takuya Sobukawa
Journal: Proc. Amer. Math. Soc. 134 (2006), 2329-2334.
MSC (2000): Primary 46B70; Secondary 46E30
Posted: February 6, 2006
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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.

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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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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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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: 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
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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