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Weighted Hardy spaces and BMO spaces associated with Schrödinger operators
Author(s) -
Liu Heping,
Tang Lin,
Zhu Hua
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100323
Subject(s) - hardy space , mathematics , omega , space (punctuation) , operator (biology) , measure (data warehouse) , combinatorics , schrödinger's cat , mathematical physics , mathematical analysis , physics , quantum mechanics , chemistry , philosophy , computer science , linguistics , biochemistry , repressor , database , transcription factor , gene
In this paper, we characterize the weighted Hardy space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$H_{\mathcal {L}}^{1}(\omega )$\end{document} related to the Schrödinger operator \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {L}=-\Delta +V$\end{document} , with V a non‐negative potential satisfying a reverse Hölder inequality, by atomic decomposition and Riesz transforms. We also get a characterization of its dual space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$B\hspace*{-1.0pt}M\hspace*{-1.0pt}O_{\mathcal {L}}(\omega )$\end{document} through a weighted Carleson measure. Then we prove the boundedness of some classical operators associated to \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {L}$\end{document} on the weighted BMO space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$B\hspace*{-1.0pt}M\hspace*{-1.0pt}O_{\mathcal {L}}(\omega )$\end{document} .