COMPLEX INTERPOLATION OF Lp(C, H) SPACES WITH RESPECT TO CULLEN-REGULAR

doi:10.1007/s10473-022-0222-9

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 774-788.doi: 10.1007/s10473-022-0222-9

COMPLEX INTERPOLATION OF L^p(C, H) SPACES WITH RESPECT TO CULLEN-REGULAR

贺凯莉, 何建勋, 娄珍珍

School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

收稿日期:2020-12-24 出版日期:2022-04-25 发布日期:2022-04-22
通讯作者: Jianxun HE,E-mail:hejianxun@gzhu.edu.cn E-mail:hejianxun@gzhu.edu.cn
作者简介:Kaili HE,E-mail:kailihe@e.gzhu.edu.cn;Zhenzhen LOU,E-mail:zhenzhenlou@e.gzhu.edu.cn
基金资助:
The first author was supported by the Innovation Research for the Postgraduates of Guangzhou University (2020GDJC-D06); this research was supported by the National Natural Science Foundation of China (12071229).

COMPLEX INTERPOLATION OF L^p(C, H) SPACES WITH RESPECT TO CULLEN-REGULAR

Kaili HE, Jianxun HE, Zhenzhen LOU

School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

Received:2020-12-24 Online:2022-04-25 Published:2022-04-22
Supported by:
The first author was supported by the Innovation Research for the Postgraduates of Guangzhou University (2020GDJC-D06); this research was supported by the National Natural Science Foundation of China (12071229).

摘要/Abstract

摘要： The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^p(C, H). In the sense of Cullen-regular, we show Hadamard's three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain. In addition, two applications of the Riesz-Thorin theorem are presented. Finally, we investigate two kinds of Calderón's complex interpolation methods in L^p(C, H).

关键词: Hadamard's three-lines theorem, complex interpolation, quaternion valued function space, Cullen-regular

Abstract: The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^p(C, H). In the sense of Cullen-regular, we show Hadamard's three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain. In addition, two applications of the Riesz-Thorin theorem are presented. Finally, we investigate two kinds of Calderón's complex interpolation methods in L^p(C, H).

Key words: Hadamard's three-lines theorem, complex interpolation, quaternion valued function space, Cullen-regular

中图分类号:

42A85

贺凯莉, 何建勋, 娄珍珍. COMPLEX INTERPOLATION OF L^p(C, H) SPACES WITH RESPECT TO CULLEN-REGULAR[J]. 数学物理学报(英文版), 2022, 42(2): 774-788.

Kaili HE, Jianxun HE, Zhenzhen LOU. COMPLEX INTERPOLATION OF L^p(C, H) SPACES WITH RESPECT TO CULLEN-REGULAR[J]. Acta mathematica scientia,Series B, 2022, 42(2): 774-788.

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COMPLEX INTERPOLATION OF L^p(C, H) SPACES WITH RESPECT TO CULLEN-REGULAR

COMPLEX INTERPOLATION OF L^p(C, H) SPACES WITH RESPECT TO CULLEN-REGULAR

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