Acta mathematica scientia, Series B >
INTERPOLATION OF LORENTZ-ORLICZ MARTINGALE SPACES
Received date: 2015-01-23
Revised date: 2014-06-27
Online published: 2015-11-01
Supported by
This work was supported by National Natural Science Foundation of China (Grant No. 11201354), by Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Y201321) and by National Natural Science Foundation of Pre-Research Item (2011XG005).
In this paper, we apply function parameters to real interpolation of Lorentz-Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces Λα introduced by Sharpley.
Key words： martingale; Lorentz-Orlicz space; interpolation; function parameter
Chuanzhou ZHANG , Yu PAN , Xueying ZHANG . INTERPOLATION OF LORENTZ-ORLICZ MARTINGALE SPACES[J]. Acta mathematica scientia, Series B, 2015 , 35(6) : 1467 -1474 . DOI: 10.1016/S0252-9602(15)30067-9
[1] Lions J L, Peetre J. Sur une classe despances dinterpolation. Inst Hautes Etudes Sci Publ Math, 1964, 19: 5-68
[2] Kalugina T F. Interpolation of Banach spaces with a functional parameter. The reiteration theorem. Vestnik Moskov Univ Ser I, Math Meh, 1975, 30(6): 68-77
[3] Gaustavsson J. A function parameter in connection with interpolation of Banach spaces. Math Scand, 1978, 42: 289-305
[4] Heinig H P. Interpolation of quasi-normed spaces involving weights. Can Math Soc, Conf Proc, 1975, 1: 245-267
[5] Merucci C. Applications of interpolation with a function parameter to Lorentz. Sobolev and Besov spaces. Lecture Note Math, 1984, 1070: 183-201
[6] Soria J. Tent Spaces Based on Weighted Lorentz Spaces, Carleson Measures [D]. Washington University, 1990
[7] Weisz F. Martingale Hardy Spaces and their Applications in Fourier Analysis. Lecture Notes in Math, 1568. New York: Springer, 1994
[8] Long R L. Martingale Spaces and Inequalities. Beijing: Peking University Press, 1993
[9] Peetre J. A Theory of Interpolation of Normed Spaces. Lecture Notes, Brasilia, 1963
[10] Sharpley R. Spaces Λα(X) and interpolation. J Funct Anal, 1972, 11: 479-513
[11] Echandia V, Finol C, Maligranda L. Interpolation of some space of Orlicz type I. Bull Polish Acad Sci Math, 1990, 38: 125-134
[12] Liu P D. Martingale and Geometry of Banach Space. Beijing: Science Press, 2007
[13] Ren Y B. Interpolation theorems for Lorentz martingale spaces. Acta Math Hungar, 2012, 134(1/2): 169-176
[14] Ren Y B, Guo T X. Interpolation of Lorentz martingale spaces. Science China Mathematics, 2012, 55(9): 1951-1959
[15] Fan L P, Jiao Y, Liu P D. Lorentz martingale spaces and interpolations. Acta Math Sci, 2010, 30B(4): 1143-1153
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