Jun LIU , Dachun YANG , Wen YUAN . LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES[J]. Acta mathematica scientia, Series B, 2018 , 38(1) : 1 -33 . DOI: 10.1016/S0252-9602(17)30115-7

[1] Abu-Shammala W, Torchinsky A. The Hardy-Lorentz spaces H^p,q(Rⁿ). Studia Math, 2007, 182:283-294
[2] Aguilera N, Segovia C. Weighted norm inequalities relating the g_λ^* and the area functions. Studia Math, 1977, 61:293-303
[3] Almeida A, Caetano A M. Generalized Hardy spaces. Acta Math Sci Ser B Engl Ed, 2010, 26:1673-1692
[4] Álvarez J. H^p and weak H^p continuity of Calderón-Zygmund type operators//Fourier Analysis, Lecture Notes in Pure and Appl Math, 157. New York:Dekker, 1994:17-34
[5] Álvarez J. Continuity properties for linear commutators of Calderón-Zygmund operators. Collect Math, 1988, 49:17-31
[6] Álvarez J, Milman M. Hp continuity properties of Calderón-Zygmund-type operators. J Math Anal Appl, 1986, 118:63-79
[7] Aoki T. Locally bounded linear topological spaces. Proc Imp Acad Tokyo, 1942, 18:588-594
[8] Bennett C, Sharpley R. Interpolation of Operators, Pure and Applied Math, 129. Orlando, FL:Academic Press, 1988
[9] Bergh J, Löfström J. Interpolation Spaces:An Introduction, Grundlehren der Mathematischen Wissenschaften, 223. Berlin-New York:Springer-Verlag, 1976
[10] Bownik M. Anisotropic Hardy Spaces and Wavelets. Mem Amer Math Soc, 2003, 164(781):122 pp
[11] Bownik M. Anisotropic Triebel-Lizorkin spaces with doubling measures. J Geom Anal, 2007, 17:387-424
[12] Bownik M, Ho K-P. Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces. Trans Amer Math Soc, 2006, 358:1469-1510
[13] Bownik M, Li B, Yang D, Zhou Y. Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators. Indiana Univ Math J, 2008, 57:3065-3100
[14] Bownik M, Li B, Yang D, Zhou Y. Weighted anisotropic product Hardy spaces and boundedness of sublinear operators. Math Nachr, 2010, 283:392-442
[15] Burkholder D L, Gundy R F, Silverstein M L. A maximal characterization of the class H^p. Trans Amer Math Soc, 1971, 157:137-153
[16] Calderón A-P. Intermediate spaces and interpolation, the complex method. Studia Math, 1964, 24:113-190
[17] Calderón A-P. Commutators of singular integral operators. Proc Nat Acad Sci, 1965, 53:1092-1099
[18] Calderón A-P. An atomic decomposition of distributions in parabolic H^p spaces. Adv Math, 1977, 25:216-225
[19] Calderón A-P, Torchinsky A. Parabolic maximal functions associated with a distribution. Adv Math, 1975, 16:1-64
[20] Calderón A-P, Torchinsky A. Parabolic maximal functions associated with a distribution, Ⅱ. Adv Math, 1977, 24:101-171
[21] Christ M. A T(b) theorem with remarks on analytic capacity and the Cauchy integral. Colloq Math, 1990, 60/61:601-628
[22] Coifman R R, Weiss G. Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, (French) Étude de certaines intégrales singulières, Lecture Notes in Mathematics, Vol 242. Berlin-New York:Springer-Verlag, 1971
[23] Coifman R R, Weiss G. Extensions of Hardy spaces and their use in analysis. Bull Amer Math Soc, 1977, 83:569-645
[24] Cwikel M. The dual of weak L^p. Ann Inst Fourier (Grenoble), 1975, 25:81-126
[25] Cwikel M, Fefferman C. Maximal seminorms on weak L¹. Studia Math, 1980/81, 69:149-154
[26] Cwikel M, Fefferman C. The canonical seminorm on weak L¹. Studia Math, 1984, 78:275-278
[27] Ding Y, Lan S. Anisotropic weak Hardy spaces and interpolation theorems. Sci China Ser A, 2008, 51:1690-1704
[28] Ding Y, Lu S. Hardy spaces estimates for multilinear operators with homogeneous kernels. Nagoya Math J, 2003, 170:117-133
[29] Ding Y, Lu S, Shao S. Integral operators with variable kernels on weak Hardy spaces. J Math Anal Appl, 2006, 317:127-135
[30] Ding Y, Lu S, Xue Q. Parametrized Littlewood-Paley operators on Hardy and weak Hardy spaces. Math Nachr, 2007, 280:351-363
[31] Fefferman C, Rivière N M, Sagher Y. Interpolation between H^p spaces:the real method. Trans Amer Math Soc, 1974, 191:75-81
[32] Fefferman C, Stein E M. Some maximal inequalities. Amer J Math, 1971, 93:107-115
[33] Fefferman C, Stein E M. H^p spaces of several variables. Acta Math, 1972, 129:137-193
[34] Fefferman R. A^p weights and singular integrals. Amer J Math, 1988, 110:975-987
[35] Fefferman R, Soria F. The spaces weak H¹. Studia Math, 1987, 85:1-16
[36] Folland G B, Stein E M. Hardy Spaces on Homogeneous Groups, Mathematical Notes 28. Princeton, NJ:Princeton University Press; Tokyo:University of Tokyo Press, 1982
[37] Frazier M, Jawerth B, Weiss G. Littlewood-Paley Theory and the Study of Function Spaces, CBMS Regional Conference Series in Mathematics 79. Washington, DC:Conference Board of the Mathematical Sciences; Providence, RI:American Mathematical Society, 1991
[38] Goginava U, Nagy K. Weak type inequality for the maximal operator of Walsh-Kaczmarz-Marcinkiewicz means. Acta Math Sci, 2016, 36B(2):359-370
[39] Grafakos L. Hardy space estimates for multilinear operators, Ⅱ. Mat Iberoamericana, 1992, 8:69-92
[40] Grafakos L. Classical Fourier Analysis//Graduate Texts in Mathematics 249, 3rd ed. New York:Springer, 2014
[41] Grafakos L, Liu L, Yang D. Vector-valued singular integrals and maximal functions on spaces of homogeneous type. Math Scand, 2009, 104:296-310
[42] Hunt R. On L(p, q) spaces. Enseignement Math, 1966, 12:249-276
[43] Ioku N, Ishige K, Yanagida E. Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups. J Math Pures Appl, 2015, 103(9):900-923
[44] Li B, Bownik M, Yang D. Littlewood-Paley characterization and duality of weighted anisotropic product Hardy spaces. J Funct Anal, 2014, 266:2611-2661
[45] Li B, Bownik M, Yang D, Yuan W. Duality of weighted anisotropic Besov and Triebel-Lizorkin spaces. Positivity, 2012, 16:213-244
[46] Li B, Bownik M, Yang D, Yuan W. A mean characterization of weighted anisotropic Besov and TriebelLizorkin spaces. Z Anal Anwend, 2014, 33:125-147
[47] Li B, Fan X, Yang D. Littlewood-Paley characterizations of anisotropic Hardy spaces of Musielak-Orlicz type. Taiwanese J Math, 2015, 19:279-314
[48] Liang Y, Huang J, Yang D. New real-variable characterizations of Musielak-Orlicz Hardy spaces. J Math Anal Appl, 2012, 395:413-428
[49] Lions J-L, Peetre J. Sur une classe d'espaces d'interpolation (French). Inst Hautes études Sci Publ Math, 1964, 19:5-68
[50] Littlewood J E, Paley R E A C. Theorems on Fourier series and power series. J London Math Soc, 1931, 6:230-233
[51] Liu H. The weak H^p spaces on homogeneous groups//Harmonic Analysis, Tianjin, 1988, Lecture Notes in Math, 1494. Berlin:Springer, 1991:113-118
[52] Liu J, Yang D, Yuan W. Anisotropic Hardy-Lorentz spaces and their applications. Sci China Math, 2016, 59:1669-1720
[53] Lorentz G G. Some new functional spaces. Ann Math, 1950, 51(2):37-55
[54] Lorentz G G. On the theory of spaces Λ. Pacific J Math, 1951, 1:411-429
[55] Lu S-Z. Four Lectures on Real H^p Spaces. River Edge, NJ:World Scientific Publishing Co Inc, 1995
[56] Merker J, Rakotoson J-M. Very weak solutions of Poisson's equation with singular data under Neumann boundary conditions. Calc Var Partial Differ Equ, 2015, 52:705-726
[57] Muscalu C, Tao T, Thiele C. A counterexample to a multilinear endpoint question of Christ and Kiselev. Math Res Lett, 2003, 10:237-246
[58] Oberlin R, Seeger A, Tao T, Thiele C, Wright J. A variation norm Carleson theorem. J Eur Math Soc, 2012, 14:421-464
[59] Parilov D. Two theorems on the Hardy-Lorentz classes H^1,q. (Russian) Zap Nauchn Sem S-Peterburg. Otdel Mat Inst Steklov, (POMI) 2005, 327, Issled po Linein Oper i Teor Funkts, 33:150-167, 238; translation in J Math Sci, (NY) 2006, 139:6447-6456
[60] Peetre J. Nouvelles propriétés d'espaces d'interpolation. C R Acad Sci Paris, 1963, 256:1424-1426
[61] Phuc N C. The Navier-Stokes equations in nonendpoint borderline Lorentz spaces. J Math Fluid Mech, 2015, 17:741-760
[62] Rolewicz S. On a certain class of linear metric spaces. Bull Acad Polon Sci Cl Trois, 1957, 5:471-473
[63] Sadosky C. Interpolation of Operators and Singular Integrals. Marcel Dekker Inc, 1976
[64] Schmeisser H-J, Triebel H. Topics in Fourier Analysis and Function Spaces. Chichester:John Wiley and Sons Ltd, 1987
[65] Seeger A, Tao T. Sharp Lorentz space estimates for rough operators. Math Ann, 2001, 320:381-415
[66] Stein E M. Harmonic Analysis:Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series 43. Princeton, NJ:Princeton University Press, 1993
[67] Stein E M, Weiss G. On the theory of harmonic functions of several variables, I:The theory of H^p spaces. Acta Math, 1960, 103:25-62
[68] Stein E M, Weiss G. Introduction to Fourier Analysis on Euclidean Spaces, Princeton Mathematical Series 32. Princeton, NJ:Princeton University Press, 1971
[69] Tao T, Wright J. Endpoint multiplier theorems of Marcinkiewicz type. Rev Mat Iberoamericana, 2001, 17:521-558
[70] Triebel H. Theory of Function Spaces. Basel:Birkhäuser Verlag, 1983
[71] Triebel H. Theory of Function Spaces, Ⅱ. Basel:Birkhäuser Verlag, 1992
[72] Triebel H. Theory of Function Spaces, Ⅲ. Basel:Birkhäuser Verlag, 2006
[73] Wang H. Boundedness of several integral operators with bounded variable kernels on Hardy and weak Hardy spaces. Internat J Math, 2013, 24(12):22 pp
[74] Yang Q, Chen Z, Peng L. Uniform characterization of function spaces by wavelets. Acta Math Sci, 2005, 25A(1):130-144