Classes of Hardy spaces associated with operators, duality theorem and applications |
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Authors: | Lixin Yan |
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Institution: | Department of Mathematics, Zhongshan University, Guangzhou, 510275, People's Republic of China |
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Abstract: | Let be the infinitesimal generator of an analytic semigroup on with suitable upper bounds on its heat kernels. In Auscher, Duong, and McIntosh (2005) and Duong and Yan (2005), a Hardy space and a space associated with the operator were introduced and studied. In this paper we define a class of spaces associated with the operator for a range of acting on certain spaces of Morrey-Campanato functions defined in New Morrey-Campanato spaces associated with operators and applications by Duong and Yan (2005), and they generalize the classical spaces. We then establish a duality theorem between the spaces and the Morrey-Campanato spaces in that same paper. As applications, we obtain the boundedness of fractional integrals on and give the inclusion between the classical spaces and the spaces associated with operators. |
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