Journal of the Mathematical Society of Japan

A system of conjugate functions on parabolic Bloch spaces

Yôsuke HISHIKAWA, Masaharu NISHIO, and Masahiro YAMADA

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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.


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.

Article information

J. Math. Soc. Japan, Volume 70, Number 3 (2018), 1085-1102.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K05: Heat equation
Secondary: 42A50: Conjugate functions, conjugate series, singular integrals 26A33: Fractional derivatives and integrals

parabolic operator of fractional order heat equation Bloch space conjugate function


HISHIKAWA, Yôsuke; NISHIO, Masaharu; YAMADA, Masahiro. A system of conjugate functions on parabolic Bloch spaces. J. Math. Soc. Japan 70 (2018), no. 3, 1085--1102. doi:10.2969/jmsj/74887488.

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