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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.
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참고문헌 (24)
참고문헌 신청
Emilio Acerbi / 2002 / Regularity Results for Stationary Electro-Rheological Fluids / Archive for Rational Mechanics and Analysis 164(3):213~259
Marcin Bownik / 2003 / Anisotropic Hardy spaces and wavelets / Memoirs of the American Mathematical Society 164(781):0~0
Yunmei Chen / 2006 / Variable Exponent, Linear Growth Functionals in Image Restoration / SIAM Journal on Applied Mathematics 66(4):1383~1406
R. R. Coifman / 1971 / Analyse harmonique non-commutative sur certains espaces homog`enes / Springer-Verlag
Ronald R. Coifman / 1977 / Extensions of Hardy spaces and their use in analysis / Bulletin of the American Mathematical Society 83(4):569~645
Marcin Bownik / 2003 / Anisotropic Hardy spaces and wavelets / Memoirs of the American Mathematical Society 164(781):0~0
Yunmei Chen / 2006 / Variable Exponent, Linear Growth Functionals in Image Restoration / SIAM Journal on Applied Mathematics 66(4):1383~1406
R. R. Coifman / 1971 / Analyse harmonique non-commutative sur certains espaces homog`enes / Springer-Verlag
Ronald R. Coifman / 1977 / Extensions of Hardy spaces and their use in analysis / Bulletin of the American Mathematical Society 83(4):569~645
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