Journal of the Mathematical Society of Japan

The reproducing formula with fractional orders on the parabolic Bloch space

Yôsuke HISHIKAWA

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Abstract

In this paper, we study the reproducing formula with fractional orders on the parabolic Bloch space. As an application of the reproducing formula, we characterize the dual and pre-dual spaces of parabolic Bergman spaces. Furthermore, we generalize the integral pairing, which gives the duality between the parabolic Bloch space and the parabolic Bergman space.

Article information

Source
J. Math. Soc. Japan, Volume 62, Number 4 (2010), 1219-1255.

Dates
First available in Project Euclid: 2 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1288703103

Digital Object Identifier
doi:10.2969/jmsj/06241219

Mathematical Reviews number (MathSciNet)
MR2761895

Zentralblatt MATH identifier
1213.35399

Subjects
Primary: 35K05: Heat equation
Secondary: 26A33: Fractional derivatives and integrals 26D10: Inequalities involving derivatives and differential and integral operators

Keywords
parabolic operator of fractional order Bloch space reproducing formula

Citation

HISHIKAWA, Yôsuke. The reproducing formula with fractional orders on the parabolic Bloch space. J. Math. Soc. Japan 62 (2010), no. 4, 1219--1255. doi:10.2969/jmsj/06241219. https://projecteuclid.org/euclid.jmsj/1288703103


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References

  • Y. Hishikawa, Fractional calculus on parabolic Bergman spaces, Hiroshima Math. J., 38 (2008), 471–488.
    Mathematical Reviews (MathSciNet): MR2477755
    Project Euclid: euclid.hmj/1233152783
  • Y. Hishikawa, M. Nishio and M. Yamada, A conjugate system and tangential derivative norms on parabolic Bergman spaces, Hokkaido Math. J., 39 (2010), 85–114.
    Mathematical Reviews (MathSciNet): MR2649328
    Digital Object Identifier: doi:10.14492/hokmj/1274275021
    Project Euclid: euclid.hokmj/1274275021
  • M. Nishio, N. Suzuki and M. Yamada, Toeplitz operators and Carleson measures on parabolic Bergman spaces, Hokkaido Math. J., 36 (2007), 567–587.
    Mathematical Reviews (MathSciNet): MR2353640
    Digital Object Identifier: doi:10.14492/hokmj/1277472867
    Project Euclid: euclid.hokmj/1277472867
  • M. Nishio, K. Shimomura and N. Suzuki, $\alpha$-parabolic Bergman spaces, Osaka J. Math., 42 (2005), 133–162.
    Mathematical Reviews (MathSciNet): MR2132007
    Project Euclid: euclid.ojm/1153494318
  • W. Ramey and H. Yi, Harmonic Bergman functions on half-spaces, Trans. Amer. Math. Soc., 348 (1996), 633–660.
    Mathematical Reviews (MathSciNet): MR1303125
    Digital Object Identifier: doi:10.1090/S0002-9947-96-01383-9
  • M. Yamada, Harmonic conjugates of parabolic Bergman functions, Advanced Studies Pure Math., 44 (2006), 391–402.
    Mathematical Reviews (MathSciNet): MR2279771

Mathematical Society of Japan

Journal of the Mathematical Society of Japan

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