Martingale inequalities and fractional integral operator in variable Hardy-Lorentz spaces

[1]  Y. Jiao,et al.  Hardy–Lorentz spaces for B-valued martingales , 2017 .

[2]  L. Pick,et al.  On embeddings between classical Lorentz spaces , 2001 .

[3]  Variable martingale Hardy spaces and their applications in Fourier analysis , 2018, Dissertationes Mathematicae.

[4]  Y. Jiao,et al.  Weak type inequalities on Lorentz martingale spaces , 2009 .

[5]  E. Nakai,et al.  Martingale Morrey-Campanato Spaces and Fractional Integrals , 2012 .

[6]  J. Antezana,et al.  Weak-Type Boundedness of the Hardy–Littlewood Maximal Operator on Weighted Lorentz Spaces , 2016, Journal of Fourier Analysis and Applications.

[7]  Wael Abu-Shammala,et al.  The Hardy-Lorentz Spaces $H^{p,q}(R^n)$ , 2007, 0704.0054.

[8]  N. Kalton,et al.  Multilinear paraproducts revisited , 2015 .

[9]  Xianling Fan,et al.  On the Spaces Lp(x)(Ω) and Wm, p(x)(Ω) , 2001 .

[10]  S. Samko,et al.  Fractional, Maximal and Singular Operators in Variable Exponent Lorentz Spaces , 2008, 0805.0693.

[11]  D. Cruz-Uribe,et al.  The fractional maximal operator and fractional integrals on variable $L^p$ spaces , 2007 .

[12]  Y. Jiao,et al.  Fractional Integral on Martingale Hardy Spaces With Variable Exponents , 2015 .

[13]  Alberto Fiorenza,et al.  Variable Lebesgue Spaces , 2013 .

[14]  Peng Lihua,et al.  Atomic decompositions of Lorentz martingale spaces and applications , 2009 .

[15]  F. Weisz.  DUAL SPACES OF MULTI-PARAMETER MARTINGALE HARDY SPACES , 2016 .

[16]  B. Muckenhoupt,et al.  Maximal functions on classical Lorentz spaces and Hardy’s inequality with weights for nonincreasing functions , 1990 .

[17]  S. Samko,et al.  Singular integrals and potentials in some Banach function spaces with variable exponent , 2003 .

[18]  Y. Jiao,et al.  Variable Hardy–Lorentz spaces associated to operators satisfying Davies–Gaffney estimates , 2019, Banach Journal of Mathematical Analysis.

[19]  George G. Lorentz,et al.  Some New Functional Spaces , 1950 .

[20]  Yonggeun Cho,et al.  Lorentz space extension of Strichartz estimates , 2005 .

[21]  Jöran Bergh,et al.  Interpolation Spaces: An Introduction , 2011 .

[22]  Y. Jiao,et al.  Variable Hardy–Lorentz spaces Hp(·),q(Rn) , 2018, Mathematische Nachrichten.

[23]  Dachun Yang,et al.  Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation , 2017, 1705.05188.

[24]  J. Chao,et al.  Commutators on dyadic martingales , 1985 .

[25]  Y. Jiao,et al.  The predual and John-Nirenberg inequalities on generalized BMO martingale spaces , 2014, 1408.4641.

[26]  Dan Zeng,et al.  New variable martingale Hardy spaces , 2022, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[27]  Jan Vyb'iral,et al.  Lorentz spaces with variable exponents , 2012, 1210.1738.

[28]  Y. Jiao,et al.  Variable martingale Hardy spaces and their applications in Fourier analysis , 1994, Dissertationes Mathematicae.

[29]  S. Samko,et al.  Hardy inequality in variable exponent Lebesgue spaces , 2007 .

[30]  Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities , 2000, math/0010010.

[31]  Gaku Sadasue,et al.  Fractional integrals on martingale Hardy spaces for 0 < p ≤ 1 , 2011 .

[32]  Y. Jiao,et al.  Riesz transform characterizations of variable Hardy–Lorentz spaces , 2018 .

[33]  K. Ho.  Atomic decompositions, dual spaces and interpolations of martingale Hardy-Lorentz-Karamata spaces , 2014 .

[34]  J. Betancor,et al.  Anisotropic Hardy-Lorentz Spaces with Variable Exponents , 2016, Canadian Journal of Mathematics.

[35]  C. Bennett,et al.  Interpolation of operators , 1987 .

[36]  Dachun Yang,et al.  Variable weak Hardy spaces and their applications , 2016, 1603.01781.

[37]  L. Grafakos.  Classical Fourier Analysis , 2010 .