Dualities of variable anisotropic Hardy spaces and boundedness of singular integral operators
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let $A$ be an expansive dilation on $\mathbb{R}^n$, and $p(\cdot):\mathbb{R}^n\rightarrow(0,\,\infty)$ be a variable exponent function satisfying the globally log-H\"{o}lder continuous condition. Let $H^{p(\cdot)}_A({\mathbb {R}}^n)$ 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 $\delta$-type Calder\'on-Zygmund operators from $H^{p(\cdot)}_{A}(\mathbb{R}^n)$ to $L^{p(\cdot)}(\mathbb{R}^n)$ or from $H^{p(\cdot)}_{A}(\mathbb{R}^n)$ to itself. In addition, the author also obtains the duality between $H^{p(\cdot)}_ A(\mathbb{R}^n)$ and the anisotropic Campanato spaces with variable exponents.
Abstract
Let $A$ be an expansive dilation on $\mathbb{R}^n$, and $p(\cdot):\mathbb{R}^n\rightarrow(0,\,\infty)$ be a variable exponent function satisfying the globally log-H\"{o}lder continuous condition. Let $H^{p(\cdot)}_A({\mathbb {R}}^n)$ 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 $\delta$-type Calder\'on-Zygmund operators from $H^{p(\cdot)}_{A}(\mathbb{R}^n)$ to $L^{p(\cdot)}(\mathbb{R}^n)$ or from $H^{p(\cdot)}_{A}(\mathbb{R}^n)$ to itself. In addition, the author also obtains the duality between $H^{p(\cdot)}_ A(\mathbb{R}^n)$ and the anisotropic Campanato spaces with variable exponents.
참고문헌 (24)
- Emilio Acerbi, "Regularity Results for Stationary Electro-Rheological Fluids", Archive for Rational Mechanics and Analysis, 164(3), pp.213~259 (2002), Springer Science and Business Media LLC[DOI]
- Marcin Bownik, "Anisotropic Hardy spaces and wavelets", Memoirs of the American Mathematical Society, 164(781), pp.0~0 (2003), American Mathematical Society (AMS)[DOI]
- Yunmei Chen, "Variable Exponent, Linear Growth Functionals in Image Restoration", SIAM Journal on Applied Mathematics, 66(4), pp.1383~1406 (2006), Society for Industrial & Applied Mathematics (SIAM)[DOI]
- R. R. Coifman, "Analyse harmonique non-commutative sur certains espaces homog`enes" (1971), Springer-Verlag
- Ronald R. Coifman, "Extensions of Hardy spaces and their use in analysis", Bulletin of the American Mathematical Society, 83(4), pp.569~645 (1977), American Mathematical Society (AMS)[DOI]
- D. V. Cruz-Uribe, "Variable Lebesgue spaces, Applied and Numerical Harmonic Analysis", pp.2013, Birkh¨auser
- David Cruz-uribe, "Variable Hardy Spaces", Indiana University Mathematics Journal, 63(2), pp.447~493 (2014), Indiana University Mathematics Journal[DOI]
- L. Diening, "Lebesgue and Sobolev spaces with variable exponents" (2011), Springer
- Xianling Fan, "Global C1,α regularity for variable exponent elliptic equations in divergence form", J. Differential Equations, 235(2), pp.397~417 (2007), Elsevier BV[DOI]
- C. Fefferman, "Hp spaces of several variables", Acta Mathematica, 129(3-4), pp.137~193 (1972), International Press of Boston[DOI]
- F. John, "On functions of bounded mean oscillation", Communications on Pure and Applied Mathematics, 14(3), pp.415~426 (1961), Wiley[DOI]
- Jun Liu, "Variable Anisotropic Hardy Spaces and Their Applications", Taiwanese Journal of Mathematics, 22(5), pp.1173~1216 (2018), The Mathematical Society of the Republic of China[DOI]
- Jun Liu, "Anisotropic Hardy-Lorentz spaces and their applications", Science China Mathematics, 59(9), pp.1669~1720 (2016), Springer Science and Business Media LLC[DOI]
- Jun Liu, "Anisotropic variable Hardy–Lorentz spaces and their real interpolation", Journal of Mathematical Analysis and Applications, 456(1), pp.356~393 (2017), Elsevier BV[DOI]
- Eiichi Nakai, "Hardy spaces with variable exponents and generalized Campanato spaces", Journal of Functional Analysis, 262(9), pp.3665~3748 (2012), Elsevier BV[DOI]
- Yoshihiro Sawano, "Atomic Decompositions of Hardy Spaces with Variable Exponents and its Application to Bounded Linear Operators", Integral Equations and Operator Theory, 77(1), pp.123~148 (2013), Springer Science and Business Media LLC[DOI]
- E. M. Stein, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" (1993), Princeton University Press
- Elias M. Stein, "On the theory of harmonic functions of several variables: I. The theory of Hp-spaces", Acta Mathematica, 103(1-2), pp.25~62 (1960), International Press of Boston[DOI]
- J. -O. Str¨omberg, "Weighted Hardy spaces" (1989), Springer-Verlag
- Jian Tan, "Atomic Decompositions of Localized Hardy Spaces with Variable Exponents and Applications", The Journal of Geometric Analysis, 29(1), pp.799~827 (2019), Springer Science and Business Media LLC[DOI]
- Tang Lin, "Lp(·),λ(·)regularity for fully nonlinear elliptic equations", Nonlinear Anal, 149, pp.117~129 (2017), Elsevier BV[DOI]
- Dachun Yang, "Characterizations of variable exponent Hardy spaces via Riesz transforms", Revista Matemática Complutense, 29(2), pp.245~270 (2016), Springer Science and Business Media LLC[DOI]
- H. Zhao, "Anisotropic Herz-type Hardy spaces with variable exponent and their applications", Acta Mathematica Hungarica, 156(2), pp.309~335 (2018), Springer Science and Business Media LLC[DOI]
- Ciqiang Zhuo, "Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents", Bulletin of the Malaysian Mathematical Sciences Society, 39(4), pp.1541~1577 (2016), Springer Science and Business Media LLC[DOI]