Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (2): 774-788.doi: 10.1007/s10473-022-0222-9

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

Kaili HE, Jianxun HE, Zhenzhen LOU   

  1. 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).

Abstract: The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on Lp(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 Lp(C, H).

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

CLC Number: 

  • 42A85
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