Hiroshima Mathematical Journal

Fractional calculus on parabolic Bergman spaces

Yôsuke Hishikawa

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

https://projecteuclid.org/euclid.hmj/1233152783

Digital Object Identifier
doi:10.32917/hmj/1233152783

Mathematical Reviews number (MathSciNet)
MR2477755

Zentralblatt MATH identifier
1200.35004

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