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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spectral multiplier theorem for $H^1$ spaces associated with some Schrödinger operators
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by Jacek Dziubański PDF
Proc. Amer. Math. Soc. 127 (1999), 3605-3613 Request permission

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 Dziubański
  • Affiliation: Institute of Mathematics, University of Wrocław, Plac Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Email: jdziuban@math.uni.wroc.pl
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3605-3613
  • MSC (1991): Primary 42B30, 35J10; Secondary 42B15, 42B25, 43A80
  • DOI: https://doi.org/10.1090/S0002-9939-99-05413-1
  • MathSciNet review: 1676352