Abstract
In this paper we introduce and study the anisotropic local Hardy spaces \(h_{A}^{p}(\mathbb{R}^{n})\) 0<p≤1, associated with the expansive matrix A. We obtain an atomic characterization of the distributions in \(h_{A}^{p}(\mathbb{R}^{n})\). Also we describe the dual spaces of our local Hardy anisotropic spaces as anisotropic Campanato type spaces.
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References
Bownik, M.: Anisotropic Hardy spaces and wavelets. Mem. Am. Math. Soc. 164(781), 1–122 (2003)
Bownik, M.: Anisotropic Triebel-Lizorkin spaces with doubling measures. J. Geom. Anal. 17(3), 387–424 (2007)
Bownik, M., Ho, K.-P.: Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces. Trans. Am. Math. Soc. 358(4), 1469–1510 (2005)
Bownik, M., Li, B., Yang, D., Zhong, Y.: Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators. Indiana Univ. Math. J. 57(7), 3065–3100 (2008)
Bui, H.-Q.: Weighted Hardy spaces. Math. Nachr. 103, 45–62 (1981)
Calderón, A.P.: An atomic decomposition of distributions in parabolic H p spaces. Adv. Math. 25, 216–225 (1977)
Calderón, A.P., Torchinsky, A.: Parabolic maximal functions associated with a distribution. Adv. Math. 16, 1–64 (1975)
Calderón, A.P., Torchinsky, A.: Parabolic maximal functions associated with a distribution, II. Adv. Math. 24, 101–171 (1977)
Coifman, R.R.: A real variable characterization of H p. Stud. Math. 51, 269–274 (1974)
Duren, P.L., Romberg, B.W., Shields, A.L.: Linear functionals on H p spaces with 0<p<1. J. Reine Angew. Math. 238, 32–60 (1969)
Fefferman, Ch.: Harmonic Analysis and H p spaces. In: Studies in Harmonic Analysis, Proc. Conf., De Paul Univ., Chicago, Ill, 1974. MAA Stud. Math., vol. 13, pp. 38–75. Math. Assoc. Am., Washington (1976)
Fefferman, C.H., Stein, E.: H p spaces of several variables. Acta Math. 129, 137–193 (1972)
Folland, G.B., Stein, E.M.: H p Spaces on Spaces on Homogeneous Group. Mathematical Notes, vol. 28. Princeton University Press/University of Tokyo Press, Princeton/Tokyo (1982)
Goldberg, D.: A local version of real Hardy spaces. Duke Math. J. 46(1), 27–42 (1979)
Ho, K.-P.: Anisotropic function spaces. Ph.D. Dissertation, Washington University (2002)
Latter, R.H.: A characterization of H p(ℝ) in terms of atoms. Stud. Math. 62, 93–101 (1978)
Stein, E.: Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, Princeton (1993)
Walsh, T.: The dual of \(H^{p}(\mathbb{R}^{n+1}_{+})\) for p<1. Can. J. Math. 25, 567–577 (1973)
Wang, H.G., Yang, X.M.: The characterization of weighted local Hardy spaces on domains and its applications. J. Zhejiang Univ. Sci. 5(9), 1148–1154 (2004)
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Communicated by Hans G. Feichtinger.
This paper is partially supported by MTM2007/65609.
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Betancor, J.J., Damián, W. Anisotropic Local Hardy Spaces. J Fourier Anal Appl 16, 658–675 (2010). https://doi.org/10.1007/s00041-010-9121-x
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DOI: https://doi.org/10.1007/s00041-010-9121-x