Molecular characterizations of variable anisotropic Hardy spaces with applications to boundedness of Calderón–Zygmund operators

Almeida, V., Betancor, J.J., Rodríguez-Mesa, L.: Anisotropic Hardy-Lorentz spaces with variable exponents. Can. J. Math. 69(6), 1219–1273 (2017)

Almeida, A., Hästö, P.: Besov spaces with variable smoothness and integrability. J. Funct. Anal. 258(5), 1628–1655 (2010)

Barrios, B., Betancor, J.J.: Anisotropic weak Hardy spaces and wavelets. J. Funct. Spaces Appl. Art. ID 809121, 17 pp (2012)

Bownik, M., Li, B., Li, J.: Variable anisotropic singular integral operators. Preprint (2020); arXiv:2004.09707 [math.FA]

Bownik, M., Wang, L.-A.D.: A PDE characterization of anisotropic Hardy spaces. Preprint

Bownik, M.: Anisotropic Hardy spaces and wavelets. Mem. Am. Math. Soc. 164(781), vi+122pp (2003)

Bownik, M., Li, B., Yang, D., Zhou, Y.: Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators. Indiana Univ. Math. J. 57(7), 3065–3100 (2008)

Calderón, A.-P., Torchinsky, A.: Parabolic maximal functions associated with a distribution. Adv. Math. 16, 1–64 (1975)

Cleanthous, G., Georgiadis, A.G., Nielsen, M.: Molecular decomposition of anisotropic homogeneous mixed-norm spaces with applications to the boundedness of operators. Appl. Comput. Harmon. Anal. 47(2), 447–480 (2019)

Cleanthous, G., Georgiadis, A.G., Nielsen, M.: Molecular decomposition and Fourier multipliers for holomorphic Besov and Triebel-Lizorkin spaces. Monatsh. Math. 188(3), 467–493 (2019)

Coifman, R.R., Weiss, G.: Extensions of Hardy spaces and their use in analysis. Bull. Am. Math. Soc. 83(4), 569–645 (1977)

Cruz-Uribe, D.V., Fiorenza, A.: Variable Lebesgue spaces. Foundations and harmonic analysis, applied and numerical harmonic analysis, Birkhäuser. Springer, Heidelberg (2013)

Cruz-Uribe, D., Wang, L.-A.D.: Variable Hardy spaces. Indiana Univ. Math. J. 63(2), 447–493 (2014)

Dekel, S., Han, Y., Petrushev, P.: Anisotropic meshless frames on $$\mathbb{R}^n$$. J. Fourier Anal. Appl. 15(5), 634–662 (2009)

Diening, L., Harjulehto, P., Hästö, P., R$$\mathring{\rm u}$$žička, M.: Lebesgue and Sobolev spaces with variable exponents. Lecture Notes in Math. 2017, Springer, Heidelberg (2011)

Diening, L., Hästö, P., Roudenko, S.: Function spaces of variable smoothness and integrability. J. Funct. Anal. 256(6), 1731–768 (2009)

Georgiadis, A.G., Kerkyacharian, G., Kyriazis, G., Petrushev, P.: Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators. J. Fourier Anal. Appl. 25(6), 3259–3309 (2019)

Grafakos, L., Torres, R.H.: Pseudodifferential operators with homogeneous symbols. Michigan Math. J. 46(2), 261–269 (1999)

Han, Y., Lee, M.-Y., Lin, C.-C.: Atomic decomposition and boundedness of operators on weighted Hardy spaces. Can. Math. Bull. 55(2), 303–314 (2012)

Huang, L., Liu, J., Yang, D., Yuan, W.: Atomic and Littlewood-Paley characterizations of anisotropic mixed-norm Hardy spaces and their applications. J. Geom. Anal. 29(3), 1991–2067 (2019)

Jakab, T., Mitrea, M.: Parabolic initial boundary value problems in nonsmooth cylinders with data in anisotropic Besov spaces. Math. Res. Lett. 13(5–6), 825–831 (2006)

Jiao, Y., Zuo, Y., Zhou, D., Wu, L.: Variable Hardy-Lorentz spaces $$H^{p(\cdot ), q}(\mathbb{R}^n)$$. Math. Nachr. 292(2), 309–349 (2019)

Kempka, H., Vybíral, J.: Lorentz spaces with variable exponents. Math. Nachr. 287(8–9), 938–954 (2014)

Lee, M.-Y., Lin, C.-C.: The molecular characterization of weighted Hardy spaces. J. Funct. Anal. 188(2), 442–460 (2002)

Liao, M., Li, J., Li Bo, Li, Ba.: A new molecular characterization of diagonal anisotropic Musielak–Orlicz Hardy spaces, Bull. Sci. Math. (to appear)

Liu, J., Haroske, D.D., Yang, D.: New molecular characterizations of anisotropic Musielak-Orlicz Hardy spaces and their applications. J. Math. Anal. Appl. 475(2), 1341–1366 (2019)

Liu, X., Qiu, X., Li, B.: Molecular characterization of anisotropic variable Hardy-Lorentz spaces. Tohoku Math. J. (2) 72(2), 211–233 (2020)

Liu, J., Weisz, F., Yang, D., Yuan, W.: Variable anisotropic Hardy spaces and their applications. Taiwanese J. Math. 22(5), 1173–1216 (2018)

Liu, J., Yang, D., Yuan, W.: Anisotropic Hardy-Lorentz spaces and their applications. Sci. China Math. 59(9), 1669–1720 (2016)

Liu, J., Yang, D., Yuan, W.: Anisotropic variable Hardy-Lorentz spaces and their real interpolation. J. Math. Anal. Appl. 456(1), 356–393 (2017)

Li, B., Yang, D., Yuan, W.: Anisotropic Hardy spaces of Musielak-Orlicz type with applications to boundedness of sublinear operators. Sci World J 2014, 19 (2014) (Article ID 306214)

Lu, S.-Z.: Four lectures on real $$H^p$$ spaces. World Scientific Publishing Co., Inc, River Edge (1995)

Nakai, E., Sawano, Y.: Hardy spaces with variable exponents and generalized Campanato spaces. J. Funct. Anal. 262(9), 3665–3748 (2012)

Sawano, Y.: Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operator. Integral Equ. Oper. Theory 77(1), 123–148 (2013)

Stein, E.M.: Harmonic analysis: Real-Variable Methods, orthogonality, and oscillatory integrals. Princeton mathematical series 43, monographs in harmonic analysis III. Princeton University Press, Princeton (1993)

Taibleson, M.H., Weiss, G.: The molecular characterization of certain Hardy spaces. In: Representation theorems for Hardy spaces, pp. 67–149, Astérisque, 77, Soc. Math. France, Paris (1980)

Xu, J.: Variable Besov and Triebel-Lizorkin spaces. Ann. Acad. Sci. Fenn. Math. 33(2), 511–522 (2008)

Yang, D., Zhuo, C., Nakai, E.: Characterizations of variable exponent Hardy spaces via Riesz transforms. Rev. Mat. Complut. 29(2), 245–270 (2016)

Yan, X., Yang, D., Yuan, W., Zhuo, C.: Variable weak Hardy spaces and thier applications. J. Funct. Anal. 271(10), 2822–2887 (2016)

Zhuo, C., Sawano, Y., Yang, D.: Hardy spaces with variable exponents on RD-spaces and applications. Dissertationes Math. (Rozprawy Mat.) 520, 1–74 (2016)

Zhuo, C., Yang, D., Yuan, W.: Interpolation between $$H^{p(\cdot )}({\mathbb{R}^n})$$ and $$L^{\infty }(\mathbb{R}^n)$$: real method. J. Geom. Anal. 28(3), 2288–2311 (2018)