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Decompositions of Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces

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Abstract

The aim of this paper is to define the Besov–Morrey spaces and the Triebel– Lizorkin–Morrey spaces and to present a decomposition of functions belonging to these spaces. Our results contain an answer to the conjecture proposed by Mazzucato.

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References

  1. D’Ancona P. and Pierfelice V. (2005). On the wave equation with a large rough potential. J. Funct. Anal. 227(1): 30–77

    Article  MATH  MathSciNet  Google Scholar 

  2. Bownik M. and Ho K. (2006). Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces. (English summary). Trans. Am. Math. Soc. 358(4): 1469–1510

    Article  MATH  MathSciNet  Google Scholar 

  3. Frazier M. and Jawerth B. (1985). A discrete transform and decompositions of distribution spaces. Indiana Univ. Math. J. 34(4): 777–799

    Article  MATH  MathSciNet  Google Scholar 

  4. Frazier M. and Jawerth B. (1990). A discrete transform and decompositions of distribution spaces. J. Funct. Anal. 93(1): 34–170

    Article  MATH  MathSciNet  Google Scholar 

  5. Kobayashi, M.: Modulation spaces M p,q for 0 < p,q ≤ ∞. J. Funct. Spaces Appl. 4(3), 329–341 (2006)

  6. Kozono H. and Yamazaki M. (1994). Semilinear heat equations and the Navier-Stokes equations with distributions in new function spaces as initial data. Comm. Par. Diff. Equ. 19(5–6): 959–1014

    Article  MATH  MathSciNet  Google Scholar 

  7. Mazzucato, A.: Decomposition of Besov–Morrey spaces. Harmonic analysis at Mount Holyoke (South Hadley, MA, 2001), 279–294, Contemp. Math., 320, Amer. Math. Soc., Providence, RI (2003)

  8. Mazzucato A. (2003). Besov–Morrey spaces : Function space theory and applications to non-linear PDE. Trans. Am. Math. Soc. 355(4): 1297–1364

    Article  MATH  MathSciNet  Google Scholar 

  9. Morrey C.B. (1938). On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc. 43(1): 126–166

    Article  MATH  MathSciNet  Google Scholar 

  10. Peetre, J.: New thoughts on Besov spaces, Duke Univ. Math. Ser. I (1976), Duke Univ., Durham

  11. Sawano Y. and Tanaka H. (2005). Morrey spaces for non-doubling measures. Acta Math. Sinica. 21(6): 1535–1544

    Article  MATH  MathSciNet  Google Scholar 

  12. Tang L. and Xu J. (2005). Some properties of Morrey type Besov–Triebel spaces. Math. Nachr. 278(7–8): 904–917

    Article  MATH  MathSciNet  Google Scholar 

  13. Triebel, H.: Theory of function spaces. Birkhäuser (1983)

  14. Triebel, H.: Theory of function spaces II. Birkhäuser (1992)

  15. Triebel, H.: Fractal and Spectra. Birkhäuser (1997)

  16. Triebel, H.: The structure of functions. Birkhäuser (2001)

  17. Uchiyama A. (1982). A constructive proof of the Fefferman-Stein decomposition of BMO(R n). Acta. Math. 148: 215–241

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-Shi, Tokyo, 192-0397, Japan

    Yoshihiro Sawano & Hitoshi Tanaka

Authors
  1. Yoshihiro Sawano
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  2. Hitoshi Tanaka
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Correspondence to Yoshihiro Sawano.

Additional information

The first author is supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. The second author is supported by Fūjyukai foundation and the 21st century COE program at Graduate School of Mathematical Sciences, the University of Tokyo.

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Sawano, Y., Tanaka, H. Decompositions of Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces. Math. Z. 257, 871–905 (2007). https://doi.org/10.1007/s00209-007-0150-3

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  • DOI: https://doi.org/10.1007/s00209-007-0150-3

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