Hiroshima Mathematical Journal

Fractional calculus on parabolic Bergman spaces

Yôsuke Hishikawa

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Abstract

The parabolic Bergman space is the set of all $L^p$-solutions of the parabolic operator $L^{(\alpha)}$. In this paper, we study fractional calculus on parabolic Bergman spaces. In particular, we investigate properties of fractional derivatives of the fundamental solution of the parabolic operator. We show the reproducing property of fractional derivatives of the fundamental solution.

Article information

Source
Hiroshima Math. J., Volume 38, Number 3 (2008), 471-488.

Dates
First available in Project Euclid: 28 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1233152783

Digital Object Identifier
doi:10.32917/hmj/1233152783

Mathematical Reviews number (MathSciNet)
MR2477755

Zentralblatt MATH identifier
1200.35004

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

Keywords
Fractional derivative Bergman space parabolic operator of fractional order reproducing kernel

Citation

Hishikawa, Yôsuke. Fractional calculus on parabolic Bergman spaces. Hiroshima Math. J. 38 (2008), no. 3, 471--488. doi:10.32917/hmj/1233152783. https://projecteuclid.org/euclid.hmj/1233152783


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