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).
Kaili HE
,
Jianxun HE
,
Zhenzhen LOU
. COMPLEX INTERPOLATION OF Lp(C, H) SPACES WITH RESPECT TO CULLEN-REGULAR[J]. Acta mathematica scientia, Series B, 2022
, 42(2)
: 774
-788
.
DOI: 10.1007/s10473-022-0222-9
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