Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces
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- by Yoshihiro Sawano, Satoko Sugano and Hitoshi Tanaka PDF
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Abstract:
The action of the generalized fractional integral operators and the generalized fractional maximal operators is investigated in the framework of Morrey spaces. A typical property of the functions which belongs to Morrey spaces under pointwise multiplication by the generalized fractional integral operators and the generalized fractional maximal operators is established. The boundedness property of the fractional integral operators on the predual of Morrey spaces is shown as well. A counterexample concerning the Fefferman-Phong inequality is given by the use of the characteristic function of the Cantor set.References
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Additional Information
- Yoshihiro Sawano
- Affiliation: Department of Mathematics, Kyoto University, Kitasirakawa, Sakyoku, Kyoto, 606-8502, Japan
- MR Author ID: 766323
- Email: yosihiro@math.kyoto-u.ac.jp
- Satoko Sugano
- Affiliation: Department of Mathematics, Kobe City College of Technology, 8-3 Gakuen-higashi- machi, Nishi-ku, Kobe 651-2194, Japan
- Email: sugano@kobe-kosen.ac.jp
- Hitoshi Tanaka
- Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
- Email: htanaka@ms.u-tokyo.ac.jp
- Received by editor(s): July 16, 2008
- Received by editor(s) in revised form: December 22, 2009
- Published electronically: July 26, 2011
- Additional Notes: The third author was supported by the Global COE program at the Graduate School of Mathematical Sciences at the University of Tokyo, and was also supported by the Fūjyukai Foundation.
- © Copyright 2011 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 6481-6503
- MSC (2010): Primary 42B35; Secondary 42B25
- DOI: https://doi.org/10.1090/S0002-9947-2011-05294-3
- MathSciNet review: 2833565