Open Access
July, 2018 A system of conjugate functions on parabolic Bloch spaces
Yôsuke HISHIKAWA, Masaharu NISHIO, Masahiro YAMADA
J. Math. Soc. Japan 70(3): 1085-1102 (July, 2018). DOI: 10.2969/jmsj/74887488


The parabolic Bloch space is the set of all solutions $u$ of the parabolic operator $L^{(\alpha)}$ with the finite Bloch norm $\| u \|_{\mathcal{B}_{\alpha} (\sigma)}$. In this paper, we introduce $L^{(\alpha)}$-conjugates of parabolic Bloch functions, and investigate several properties. As an application, we give an isomorphism theorem on parabolic Bloch spaces.

Funding Statement

This work was supported in part by Grant-in-Aid for Scientific Research (C) No.16K05198 and No.15K04934, Japan Society for the Promotion of Science.


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Yôsuke HISHIKAWA. Masaharu NISHIO. Masahiro YAMADA. "A system of conjugate functions on parabolic Bloch spaces." J. Math. Soc. Japan 70 (3) 1085 - 1102, July, 2018.


Received: 12 April 2016; Revised: 10 January 2017; Published: July, 2018
First available in Project Euclid: 18 June 2018

zbMATH: 06966975
MathSciNet: MR3830800
Digital Object Identifier: 10.2969/jmsj/74887488

Primary: 35K05
Secondary: 26A33 , 42A50

Keywords: Bloch space , conjugate function , heat equation , parabolic operator of fractional order

Rights: Copyright © 2018 Mathematical Society of Japan

Vol.70 • No. 3 • July, 2018
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