Acta mathematica scientia, Series B >
MONOTONICITY IN ORLICZ-LORENTZ SEQUENCE SPACES EQUIPPED WITH THE ORLICZ NORM
Received date: 2015-06-25
Revised date: 2016-05-05
Online published: 2016-12-25
Supported by
This work was supported by the National Science Foundation of China (11271248 and 11302002), the National Science Research Project of Anhui Educational Department (KJ2012Z127), and the PhD research startup foundation of Anhui Normal University.
In Orlicz-Lorentz sequence space λ ?,ω° with the Orlicz norm, uniform monotonicity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in λ ?,ω° are discussed.
Wanzhong GONG , Daoxiang ZHANG . MONOTONICITY IN ORLICZ-LORENTZ SEQUENCE SPACES EQUIPPED WITH THE ORLICZ NORM[J]. Acta mathematica scientia, Series B, 2016 , 36(6) : 1577 -1589 . DOI: 10.1016/S0252-9602(16)30091-1
[1] Kurc W. Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation. J Approx Theory, 1992, 69:173-187
[2] Hudzik H, Liu X B, Wang T F. Points of monotonicity in Musielak-Orlicz function spaces endowed with the Luxemburg norm. Arch Math, 2004, 82:534-545
[3] Hudzik H, Kurc W. Monotonicity properties of Musielak-Orlicz spaces and domained best approximation in Banach lattices. J Approx Theory, 1998, 95:353-368
[4] Birkhoff G. Lattice Theory. Providence, RI:Amer Math Soc, 1988
[5] Lü Y M, Wang J M, Wang T F. Monotone coefficients and monotonicity of Orlicz spaces. Rev Mat Complut, 1999, 12:105-114
[6] Chen S T, He X, Hudzik H, Kamińska A. Monotonicity and best approximation in Orlicz-Sobolev spaces with the Luxemburg norm. J Math Anal Appl, 2008, 344:687-698
[7] Hudzik H, Kamińska A. Monotonicity properties of Lorentz spaces. Proc Amer Math Soc, 1995, 123:2715-2721
[8] Kolwicz P. Rotundity properties in Calderón-Lozanovski? spaces. Houston J Math, 2005, 31:883-912
[9] Wang J C, Ning Z. Rotundtity and uniform rotundity of Orlicz-Lorentz sequence spaces with the Orlicz norm. Math Nachr, 2011, 284:2297-2311
[10] Kamińska A. Some remarks on Orlicz-Lorentz spaces. Math Nachr, 1990, 147:29-38
[11] Chen S T. Geometry of Orlicz spaces. Dissertationes Math, 356, 1996
[12] Bennett C, Sharpley R. Interpolation of Operators. New York:University of Sorth Carolina, 1988
[13] Zhang C Z, Pan Y, Zhang X Y. Interpolation of Lorentz-Orlicz martingale spaces. Acta Math Sci, 2015, 35B:1467-1474
[14] Foralewski P, Hudzik H, Kaczmarek R, Krbec M. Moduli and characteristics of monotonicity in some Banach lattices. Fixed Point Theory Appl, 2010:Art ID 852346
[15] Foralewski P, Hudzik H, Kaczmarek R, Krbec M, Wójtowicz M. On the moduli and characteristic of monotonicity in Orlicz-Lorentz function spaces. J Convex Anal, 2013, 20:955-970
[16] Foralewski P, Hudzik H, Kaczmarek R, Krbec M. Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm. Comment Math, 2013, 53:421-432
[17] Cui Y A, Hudzik H, Wis la M. Monotonicity properties and dominated best approximation problems in Orlicz spaces equipped with the p-Amemiya norm. J Math Anal Appl, 2015, 432:1095-1105
[18] Hudzik H, Kaczmarek R. Monotonicity characteristic of Köthe-Bochner spaces. J Math Anal Appl, 2009, 349:459-468
[19] Chen S T, He X, Hudzik H. Monotonicity and best approximation in Banach lattices. Acta Math Sin (Engl Ser), 2009, 25:785-794
[20] Hudzik H, Narloch A, Local monotonicity structure of Calderón-Lozanovski? spaces. Indag Math, 2004, 15:245-255
[21] Hudzik H, Kaczmarek R, Krbec M. In some symmetric spaces monotonicity properties can be reduced to the cone of rearrangements. Aequationes Math, 2016, 90:249-261
[22] Hudzik H, Kurc W. Monotonicity properties of Musielak-Orlicz spaces and dominated best approximation in Banach lattices. J Approx Theory, 1998, 95:353-368
[23] Choi C, Kamińska A, Lee H. Complex convexity of Orlicz-Lorentz spaces and its applications. Bull Polish Acad Sci Math, 2004, 52:19-38
[24] Kolwicz P, P luciennik R. Points of upper local uniform monotonicity in Calderón-Lozanowski? spaces. J Convex Anal, 2010, 17:111-130
[25] Cerda J, Hudzik H, Kamińska A, Masty lo M. Geometric properties of symmetric spaces with applications to Orlicz-Lorentz spaces. Positivity, 1998, 2:311-337
[26] Foralewski P. On Some geometric properties of generalized Orlicz-Lorentz sequence spaces. Indag Math, 2013, 24:346-372
[27] Hudzik H, Kamińska A, Masty lo M. Monotonicity and rotundity properties in Banach lattices. Rocky Mountain J Math, 2000, 30:933-950
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