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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Abstract

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.

Note

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1529309024

Digital Object Identifier
doi:10.2969/jmsj/74887488

Mathematical Reviews number (MathSciNet)
MR3830800

Zentralblatt MATH identifier
06966975

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

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

Citation

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. https://projecteuclid.org/euclid.jmsj/1529309024


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