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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectral multiplier theorem for $H^1$ spaces
associated with some Schrödinger operators


Author: Jacek Dziubanski
Journal: Proc. Amer. Math. Soc. 127 (1999), 3605-3613
MSC (1991): Primary 42B30, 35J10; Secondary 42B15, 42B25, 43A80
Published electronically: July 23, 1999
MathSciNet review: 1676352
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Abstract: Let $T_{t}$ be the semigroup of linear operators generated by a Schrödinger operator $-A=\Delta -V$, where $V$ is a nonnegative polynomial. We say that $f$ is an element of $H_{A}^{1}$ if the maximal function $\mathcal{M}f(x)=\sup _{t>0} |T_{t}f(x)|$ belongs to $L^{1}$. A criterion on functions $F$ which implies boundedness of the operators $F(A)$ on $H_{A}^{1}$ is given.


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Additional Information

Jacek Dziubanski
Affiliation: Institute of Mathematics, University of Wrocław, Plac Grunwaldzki 2/4, 50-384 Wrocław, Poland
Email: jdziuban@math.uni.wroc.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05413-1
PII: S 0002-9939(99)05413-1
Received by editor(s): February 17, 1998
Published electronically: July 23, 1999
Additional Notes: This research was partially supported by the European Commission via TMR network “Harmonic Analysis", and by grant 2 P03A 058 14 from KBN, Poland.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society