Browse > Article
http://dx.doi.org/10.4134/BKMS.b200301

DUALITIES OF VARIABLE ANISOTROPIC HARDY SPACES AND BOUNDEDNESS OF SINGULAR INTEGRAL OPERATORS  

Wang, Wenhua (School of Mathematics and Statistics Wuhan University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 365-384 More about this Journal
Abstract
Let A be an expansive dilation on ℝn, and p(·) : ℝn → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. Let Hp(·)A (ℝn) be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the author obtains the boundedness of anisotropic convolutional ��-type Calderón-Zygmund operators from Hp(·)A (ℝn) to Lp(·) (ℝn) or from Hp(·)A (ℝn) to itself. In addition, the author also obtains the duality between Hp(·)A (ℝn) and the anisotropic Campanato spaces with variable exponents.
Keywords
Anisotropy; Hardy space; atom; $Calder{\acute{o}}n$-Zygmund operator; Campanato space;
Citations & Related Records
연도 인용수 순위
  • Reference
1 X. Fan, Global C1,α regularity for variable exponent elliptic equations in divergence form, J. Differential Equations 235 (2007), no. 2, 397-417. https://doi.org/10.1016/j.jde.2007.01.008   DOI
2 C. Fefferman and E. M. Stein, Hp spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137-193. https://doi.org/10.1007/BF02392215   DOI
3 F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. https://doi.org/10.1002/cpa.3160140317   DOI
4 J. Liu, F. Weisz, D. Yang, and W. Yuan, Variable anisotropic Hardy spaces and their applications, Taiwanese J. Math. 22 (2018), no. 5, 1173-1216. https://doi.org/10.11650/tjm/171101   DOI
5 J. Liu, D. Yang, and W. Yuan, Anisotropic Hardy-Lorentz spaces and their applications, Sci. China Math. 59 (2016), no. 9, 1669-1720. https://doi.org/10.1007/s11425-016-5157-y   DOI
6 J. Liu, D. Yang, and W. Yuan, Anisotropic variable Hardy-Lorentz spaces and their real interpolation, J. Math. Anal. Appl. 456 (2017), no. 1, 356-393. https://doi.org/10.1016/j.jmaa.2017.07.003   DOI
7 E. Nakai and Y. Sawano, Hardy spaces with variable exponents and generalized Campanato spaces, J. Funct. Anal. 262 (2012), no. 9, 3665-3748. https://doi.org/10.1016/j.jfa.2012.01.004   DOI
8 Y. Sawano, Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operators, Integral Equations Operator Theory 77 (2013), no. 1, 123-148. https://doi.org/10.1007/s00020-013-2073-1   DOI
9 E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, 43, Princeton University Press, Princeton, NJ, 1993.
10 E. Acerbi and G. Mingione, Regularity results for stationary electro-rheological fluids, Arch. Ration. Mech. Anal. 164 (2002), no. 3, 213-259. https://doi.org/10.1007/s00205-002-0208-7   DOI
11 M. Bownik, Anisotropic Hardy spaces and wavelets, Mem. Amer. Math. Soc. 164 (2003), no. 781, vi+122 pp. https://doi.org/10.1090/memo/0781   DOI
12 Y. Chen, S. Levine, and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006), no. 4, 1383-1406. https://doi.org/10.1137/050624522   DOI
13 R. R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogenes, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin, 1971.
14 R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569-645. https://doi.org/10.1090/S0002-9904-1977-14325-5   DOI
15 J. Tan, Atomic decompositions of localized Hardy spaces with variable exponents and applications, J. Geom. Anal. 29 (2019), no. 1, 799-827. https://doi.org/10.1007/s12220-018-0019-1   DOI
16 D. V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue spaces, Applied and Numerical Harmonic Analysis, Birkhauser/Springer, Heidelberg, 2013. https://doi.org/10.1007/978-3-0348-0548-3   DOI
17 D. Cruz-Uribe and L.-A. D. Wang, Variable Hardy spaces, Indiana Univ. Math. J. 63 (2014), no. 2, 447-493. https://doi.org/10.1512/iumj.2014.63.5232   DOI
18 L. Diening, P. Harjulehto, P. Hasto, and M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents, Lecture Notes in Mathematics, 2017, Springer, Heidelberg, 2011. https://doi.org/10.1007/978-3-642-18363-8   DOI
19 E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables. I. The theory of Hp-spaces, Acta Math. 103 (1960), 25-62. https://doi.org/10.1007/BF02546524   DOI
20 J.-O. Stromberg and A. Torchinsky, Weighted Hardy spaces, Lecture Notes in Mathematics, 1381, Springer-Verlag, Berlin, 1989. https://doi.org/10.1007/BFb0091154   DOI
21 L. Tang, Lp(·),λ(·) regularity for fully nonlinear elliptic equations, Nonlinear Anal. 149 (2017), 117-129. https://doi.org/10.1016/j.na.2016.10.016   DOI
22 D. Yang, C. Zhuo, and E. Nakai, Characterizations of variable exponent Hardy spaces via Riesz transforms, Rev. Mat. Complut. 29 (2016), no. 2, 245-270. https://doi.org/10.1007/s13163-016-0188-z   DOI
23 C. Zhuo, D. Yang, and Y. Liang, Intrinsic square function characterizations of Hardy spaces with variable exponents, Bull. Malays. Math. Sci. Soc. 39 (2016), no. 4, 1541-1577. https://doi.org/10.1007/s40840-015-0266-2   DOI
24 H. Zhao and J. Zhou, Anisotropic Herz-type Hardy spaces with variable exponent and their applications, Acta Math. Hungar. 156 (2018), no. 2, 309-335. https://doi.org/10.1007/s10474-018-0851-6   DOI