Weighted local Hardy spaces associated with operators |
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Authors: | Ruming Gong Liang Song Peizhu Xie |
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Institution: | 1.School of Mathematics and Information Science,Guangzhou University,Guangzhou,People’s Republic of China;2.Department of Mathematics,Sun Yat-sen (Zhongshan) University,Guangzhou,People’s Republic of China |
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Abstract: | Let L be a self-adjoint positive operator on \(L^2(\mathbb {R}^n)\). Assume that the semigroup \(e^{-tL}\) generated by \(-L\) satisfies the Gaussian kernel bounds on \(L^2(\mathbb {R}^n)\). In this article, we study weighted local Hardy space \(h_{L,w}^{1}(\mathbb {R}^n)\) associated with L in terms of the area function characterization, and prove their atomic characters. Then, we introduce the weighted local BMO space \(\mathrm{bmo}_{L,w}(\mathbb {R}^n)\) and prove that the dual of \(h_{L,w}^{1}(\mathbb {R}^n)\) is \(\mathrm{bmo}_{L,w}(\mathbb {R}^n)\). Finally a broad class of applications of these results is described. |
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