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November 2021 Function spaces induced by two parabolic Bloch spaces
Yôsuke Hishikawa, Masaharu Nishio, Katsunori Shimomura, Masahiro Yamada
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Hiroshima Math. J. 51(3): 247-265 (November 2021). DOI: 10.32917/h2020031


We consider function spaces which consist of two parabolic Bloch spaces, and present reproducing formulas. As an application, we introduce Bloch type spaces which consist of solutions of a partial differential equation $(L^{(\alpha)})^2u=0$, and investigate several properties.

Funding Statement

The Second and Third authors are supported by Grant-in-aid for Science Research, No. JP19K03523.
The Fourth author is supported by Grant-in-aid for Science Research, No. JP16K05198.


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Yôsuke Hishikawa. Masaharu Nishio. Katsunori Shimomura. Masahiro Yamada. "Function spaces induced by two parabolic Bloch spaces." Hiroshima Math. J. 51 (3) 247 - 265, November 2021.


Received: 26 April 2020; Revised: 19 February 2021; Published: November 2021
First available in Project Euclid: 1 December 2021

Digital Object Identifier: 10.32917/h2020031

Primary: 35K05
Secondary: 26A33 , 30H30

Keywords: Bloch space , fractional order , reproducing kernel

Rights: Copyright © 2021 Hiroshima University, Mathematics Program


Vol.51 • No. 3 • November 2021
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