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

doi:10.1007/s10473-022-0222-9

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 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).

Abstract

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

CLC Number:

42A85

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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References

[1] Riesz M. Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires. Acta Math, 1927, 49(3/4):465-497
[2] Thorin G O. Convexity theorems generalizing those of M. Riesz and Hadamard with some applications. Medd Lunds Univ Mat Sem, 1948, 9:1-58
[3] Tamarkin J D, Zygmund A. Proof of a theorem of Thorin. Bull Amer Math Soc, 1944, 50:279-282
[4] Lions J L. Une construction d'espaces d'interpolation. C R Acad Sci Paris, 1960, 251:1853-1855
[5] Bergh J, Löfström J. Interpolation spaces. An introduction. Berlin-New York:Springer-Verlag, 1976
[6] Grafakos L. L^p Spaces and Interpolation. New York:Springer, 2008
[7] Calderón A P. Intermediate spaces and interpolation, the complex method. Studia Math, 1964, 24:113-190
[8] Fueter R. Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen. Comment Math Helv, 1935, 8(1):371-378
[9] Sudbery A. Quaternionic analysis. Math Proc Cambridge Philos Soc, 1979, 85(2):199-224
[10] Ghiloni R, Perotti A. Slice regular functions on real alternative algebras. Adv Math, 2011, 226(2):1662- 1691
[11] Cullen C G. An integral theorem for analytic intrinsic functions on quaternions. Duke Math J, 1965, 32:139-148
[12] Gentili G, Struppa D C. A new approach to Cullen-regular functions of a quaternionic variable. C R Math Acad Sci Paris, 2006, 342(10):741-744
[13] Gentili G, Struppa D C. A new theory of regular functions of a quaternionic variable. Adv Math, 2007, 216(1):279-301
[14] Gentili G, Stoppato C, Struppa D C. Regular functions of a quaternionic variable. Heidelberg:Springer, 2013
[15] Hitzer E M S. Quaternion Fourier transform on quaternion fields and generalizations. Adv Appl Clifford Algebr, 2007, 17(3):497-517
[16] Moxey C E, Sangwine S J, Ell T A. Hypercomplex correlation techniques for vector images. IEEE Trans Signal Process, 2003, 51(7):1941-1953
[17] Qiao L H, Niu K F, Wang N, et al. Perfect reconstruction image modulation based on BEMD and quaternionic analytic signals. Sci China Inf Sci, 2011, 54(12):2602-2614
[18] Akila L. Quaternionic integral transforms and their generalizations[D]. India:Alagappa University, 2016
[19] Akila L, Roopkumar R. A nature convolution of quaternion valued functions and its applications. Appl Math Comput, 2014, 242:633-642
[20] Grafakos L. Classical Fourier analysis. New York:Springer, 2014

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

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