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.
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.
Citation
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. https://doi.org/10.2969/jmsj/74887488
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