Abstract
In this paper we introduce molecules associated to Hardy spaces with pointwise variable anisotropy. We establish molecular characterizations of such Hardy spaces with pointwise variable anisotropy.
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Barrios, B., Betancor, J.J.: Anisotropic weak Hardy spaces and wavelets. J. Funct. Spaces Appl. Article ID 809121, 17 (2012)
Betancor, J.J., Damián, W.: Anisotropic local Hardy spaces. J. Fourier Anal. Appl. 16, 658–675 (2010)
Bownik, M.: Anisotropic Hardy spaces and wavelets. Mem. Am. Math. Soc. 164, vi+122 (2003)
Bownik, M.: Boundedness of operators on Hardy spaces via atomic decompositions. Proc. Am. Math. Soc. 133, 3535–3542 (2005)
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, 3065–3100 (2008)
Coifman, R.R., Weiss, G.: Analyse harmonique non-commutative sur certains espaces homogènes. Lecture Notes in Mathematics, vol. 242. Springer, Berlin (1971)
Coifman, R.R., Weiss, G.: Extensions of Hardy spaces and their use in analysis. Bull. Am. Math. Soc. 83, 569–645 (1977)
Dahmen, W., Dekel, S., Petrushev, P.: Two-level-split decomposition of anisotropic Besov spaces. Constr. Approx. 31, 149–194 (2010)
Dekel, S., Petrushev, P., Weissblat, T.: Hardy spaces on \({\mathbb{R}}^n\) with pointwise variable anisotropy. J. Fourier Anal. Appl. 17, 1066–1107 (2011)
Dekel, S., Weissblat, T.: On dual spaces of anisotropic Hardy spaces. Math. Nachr. 285, 2078–2092 (2012)
Grafakos, L., Liu, L., Yang, D.: Maximal function characterizations of Hardy spaces on RD-spaces and their applications. Sci. China Ser. A 51, 2253–2284 (2008)
Han, Y., Müller, D., Yang, D.: Littlewood–Paley characterizations for Hardy spaces on spaces of homogeneous type. Math. Nachr. 279, 1505–1537 (2006)
Hu, G.: Littlewood–Paley characterization of weighted anisotropic Hardy spaces. Taiwan. J. Math. 17, 675–700 (2013)
Lee, M.-Y., Lin, C.-C.: The molecular characterization of weighted Hardy spaces. J. Funct. Anal. 188, 442–460 (2002)
Li, X., Peng, L.: The molecular characterization of weighted Hardy spaces. Sci. China Ser. A 44, 201–211 (2001)
Macías, R.A., Segovia, C.: A decomposition into atoms of distributions on spaces of homogeneous type. Adv. Math. 33, 271–309 (1979)
Serra, C.F.: Molecular characterization of Hardy–Orlicz spaces. Rev. Un. Mat. Argent. 40, 203–217 (1996)
Stein, E.M.: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, Princeton (1993)
Taibleson, M.H., Weiss, G.: The molecular characterization of Hardy spaces. In Harmonic Analysis in Euclidean Spaces (Proceedings of Sympososium on Pure Mathematics, Williams College, Williamstown, 1978), Part 1, Proceendings of Symposium Pure Mathematics, XXXV, Part, American Mathematical Society, Providence, pp. 281–287 (1979)
Taibleson, M.H., Weiss, G.: The molecular characterization of certain Hardy spaces. In: Kahane, J.P. (ed.) Representation Theorems for Hardy Spaces, Astérisque, vol. 77, pp. 67–149. Soc. Math. France, Paris (1980)
Wang, L.-A.D.: Multiplier theorems on anisotropic Hardy spaces, ProQuest LLC, Ann Arbor, MI. Thesis (Ph.D.), University of Oregon (2012)
Zhao, K., Li, L.-L.: Molecular decomposition of weighted anisotropic Hardy spaces. Taiwan. J. Math. 17, 583–599 (2013)
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This paper is partially supported by MTM2013-44357-P and MTM2016-79436-P.
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Almeida, V., Betancor, J.J. & Rodríguez-Mesa, L. Molecules Associated to Hardy Spaces with Pointwise Variable Anisotropy. Integr. Equ. Oper. Theory 89, 301–313 (2017). https://doi.org/10.1007/s00020-017-2403-9
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DOI: https://doi.org/10.1007/s00020-017-2403-9