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Operator–valued Fourier Multipliers on Periodic Triebel Spaces

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Abstract

We establish operator–valued Fourier multiplier theorems on periodic Triebel spaces, where the required smoothness of the multipliers depends on the indices of the Triebel spaces. This is used to give a characterization of the maximal regularity in the sense of Triebel spaces for Cauchy problems with periodic boundary conditions.

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References

  1. Amann, H.: Operator–valued Fourier multipliers, vector–valued Besov spaces, and applications. Math. Nachr., 186, 5–56 (1997)

    MathSciNet  Google Scholar 

  2. Arendt, W., Bu, S.: Operator–valued Fourier multipliers on Besov spaces and applications. Proc. Edinburgh Math. Soc., 47, 15–33 (2004)

    Article  MathSciNet  Google Scholar 

  3. Arendt, W., Bu, S.: The operator–valued Marcinkiewicz multiplier theorem and maximal regularity. Math. Z., 240, 311–343 (2002)

    Article  MathSciNet  Google Scholar 

  4. Girardi, M., Weis, L.: Operator–valued Fourier multiplier theorems on Besov spaces. Math. Nachr., 251, 34–51 (2003)

    Article  MathSciNet  Google Scholar 

  5. Weis, L.: Operator–valued Fourier multiplier theorems and maximal L p –regularity. Math. Ann., 319, 735–758 (2001)

    Article  MathSciNet  Google Scholar 

  6. Zimmermann, F.: On vector–valued Fourier multiplier theorems. Studia Math., 93, 201–222 (1989)

    MathSciNet  Google Scholar 

  7. Arendt, W., Bu, S.: Tools for maximal regularity. Math. Proc. Cambridge Phil., 134, 317–336 (2003)

    MathSciNet  Google Scholar 

  8. Weis, L.: A new approach to maximal L p –regularity. In: Evoluequations and their applications in physical and life sciences (Bad Herrenalb 1998) Dekker, New York 195–214, 2001

  9. Edwards, R. E.: Fourier Series I., Graduate Texts in Mathematics 64, Springer–Verlag, New York–Heidelberg– Berlin, 1979

  10. Schmeisser, H. J., Triebel, H.: Topics in Fourier Analysis and Function Spaces, Geest, Portig, Leipzig, 1987, Wiley, Chichester, 1987

  11. Triebel, H.: Theory of Function Spaces, Geest, Portig, Leipzig, 1983, Basel, Birkhäuser, 1983

  12. Triebel, H.: Fractals and Spectra, Birkhäuser Verlag, Basel, 1997

  13. Zygmund, A.: Trigonometric Series, Vol. II. Cambridge University Press, Cambridge, 1959

  14. Weis, L.: Stability theorems for semigroups via multiplier theorems. Differential equations, asymptotic analysis and mathematical physics (Potsdam, 1996), Akademie Verlag, Berlin, 407–411, 1997

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Authors and Affiliations

  1. Department of Mathematical Science, University of Tsinghua, Beijing 100084, P. R. China

    Shang Quan Bu & Jin Myong Kim

Authors
  1. Shang Quan Bu
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  2. Jin Myong Kim
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Corresponding authors

Correspondence to Shang Quan Bu or Jin Myong Kim.

Additional information

The first author is supported by the NSF of China and the Excellent Young Teachers Program of MOE, P.R.C.

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Bu, S.Q., Kim, J.M. Operator–valued Fourier Multipliers on Periodic Triebel Spaces. Acta Math Sinica 21, 1049–1056 (2005). https://doi.org/10.1007/s10114-004-0453-9

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  • DOI: https://doi.org/10.1007/s10114-004-0453-9

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