Real‐variable characterizations of Musielak–Orlicz–Hardy spaces associated with Schrödinger operators on domains |
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Authors: | Der‐Chen Chang Zunwei Fu Dachun Yang Sibei Yang |
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Affiliation: | 1. Department of Mathematics and Department of Computer Science, Georgetown University, Washington DC, USA;2. Department of Mathematics, Fu Jen Catholic University, Taipei, Taiwan;3. Department of Mathematics, Linyi University, Linyi, China;4. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, China;5. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu, China |
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Abstract: | Let n≥3, Ω be a strongly Lipschitz domain of and LΩ:=?Δ+V a Schrödinger operator on L2(Ω) with the Dirichlet boundary condition, where Δ is the Laplace operator and the nonnegative potential V belongs to the reverse Hölder class for some q0>n/2. Assume that the growth function satisfies that ?(x,·) is an Orlicz function, (the class of uniformly Muckenhoupt weights) and its uniformly critical lower type index , where and μ0∈(0,1] denotes the critical regularity index of the heat kernels of the Laplace operator Δ on Ω. In this article, the authors first show that the heat kernels of LΩ satisfy the Gaussian upper bound estimates and the Hölder continuity. The authors then introduce the ‘geometrical’ Musielak–Orlicz–Hardy space via , the Hardy space associated with on , and establish its several equivalent characterizations, respectively, in terms of the non‐tangential or the vertical maximal functions or the Lusin area functions associated with LΩ. All the results essentially improve the known results even on Hardy spaces with p∈(n/(n + δ),1] (in this case, ?(x,t):=tp for all x∈Ω and t∈[0,∞)). Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | Musielak– Orlicz– Hardy space Schrö dinger operator strongly Lipschitz domain Dirichlet boundary condition Gaussian upper bound maximal function Lusin area function atom subclass42B35 42B30 35J10 42B25 46E30 |
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