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Spectral Multipliers for Hardy Spaces Associated with Schrödinger Operators with Polynomial Potentials
Author(s) -
Dziubański Jacek
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609300007311
Subject(s) - mathematics , semigroup , polynomial , linear operators , operator (biology) , multiplier (economics) , schrödinger's cat , pseudodifferential operators , element (criminal law) , resolution (logic) , hardy space , type (biology) , pure mathematics , discrete mathematics , mathematical analysis , bounded function , ecology , biochemistry , chemistry , repressor , artificial intelligence , biology , political science , transcription factor , computer science , law , gene , macroeconomics , economics
Let T t be the semigroup of linear operators generated by a Schrödinger operator − A = Δ − V , where V is a non‐negative polynomial, and let∫ 0 ∞ λ d E A ( λ )be the spectral resolution of A . We say that f is an element ofH A pif the maximal function M f ( x ) = sup t >0 | T t f ( x )| belongs to L p . We prove a criterion of Mihlin type on functions F which implies boundedness of the operators F ( A ) = ∫ 0 ∞ F ( λ ) d E A ( λ )onH A p , 0 < p ⩽ 1. 1991 Mathematics Subject Classification 42B30, 35J10.