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March 2011 Function spaces of parabolic Bloch type
Yôsuke Hishikawa, Masahiro Yamada
Hiroshima Math. J. 41(1): 55-87 (March 2011). DOI: 10.32917/hmj/1301586290

Abstract

The $L^{(\alpha)}$-harmonic function is the solution of the parabolic operator $L^{(\alpha)}= \partial_{t}+(-\Delta_{x})^{\alpha}$. We study a function space $\widetilde{{\cal B}}_{\alpha}(\sigma)$ consisting of $L^{(\alpha)}$-harmonic functions of parabolic Bloch type. In particular, we give a reproducing formula for functions in $\widetilde{{\cal B}}_{\alpha}(\sigma)$. Furthermore, we study the fractional calculus on $\widetilde{{\cal B}}_{\alpha}(\sigma)$. As an application, we also give a reproducing formula with fractional orders for functions in $\widetilde{{\cal B}}_{\alpha}(\sigma)$. Moreover, we investigate the dual and pre-dual spaces of function spaces of parabolic Bloch type.

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Yôsuke Hishikawa. Masahiro Yamada. "Function spaces of parabolic Bloch type." Hiroshima Math. J. 41 (1) 55 - 87, March 2011. https://doi.org/10.32917/hmj/1301586290

Information

Published: March 2011
First available in Project Euclid: 31 March 2011

zbMATH: 1233.35199
MathSciNet: MR2809048
Digital Object Identifier: 10.32917/hmj/1301586290

Subjects:
Primary: 35K05
Secondary: 31B10, 32A18

Rights: Copyright © 2011 Hiroshima University, Mathematics Program

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Vol.41 • No. 1 • March 2011
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