Hiroshima Mathematical Journal
- Hiroshima Math. J.
- Volume 38, Number 3 (2008), 471-488.
Fractional calculus on parabolic Bergman spaces
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
