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The higher order Riesz transform and BMO type space associated to Schrödinger operators
Author(s) -
Dong Jianfeng,
Liu Yu
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.201000067
Subject(s) - mathematics , order (exchange) , space (punctuation) , type (biology) , operator (biology) , class (philosophy) , combinatorics , mathematical physics , chemistry , philosophy , ecology , linguistics , biochemistry , finance , repressor , epistemology , gene , transcription factor , economics , biology
Let L = −Δ + V be a Schrödinger operator on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}^n$\end{document} ( n ≥ 3), where \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$V \not\equiv 0$\end{document} is a nonnegative potential belonging to certain reverse Hölder class B s for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$s \ge \frac{n}{2}$\end{document} . In this article, we prove the boundedness of some integral operators related to L , such as L −1 ∇ 2 , L −1 V and L −1 ( − Δ) on the space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$BMO_L(\mathbb {R}^n)$\end{document} .