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SPECTRAL MULTIPLIERS FOR HARDY SPACES ASSOCIATED WITH SCHRÖDINGER OPERATORS WITH POLYNOMIAL POTENTIALS

Published online by Cambridge University Press:  23 October 2000

JACEK DZIUBAŃSKI
JACEK DZIUBAŃSKI
Affiliation:
Institute of Mathematics, University of Wrocław, Plac Grunwaldzki 2/4, 50-384 Wrocław, Poland; e-mail: [email protected]
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Abstract

Let Tt be the semigroup of linear operators generated by a Schrödinger operator − A = Δ − V, where V is a non-negative polynomial, and let ∫∞0λdEA(λ) be the spectral resolution of A. We say that f is an element of HpA if the maximal function [Mscr ]f(x) = supt>0[mid ]Ttf(x)[mid ] belongs to Lp. We prove a criterion of Mihlin type on functions F which implies boundedness of the operators F(A) = ∫∞0F(λ)dEA(λ) on HpA, 0 < p [les ] 1.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 5 , September 2000 , pp. 571 - 581
Copyright
© The London Mathematical Society 2000

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Footnotes

Research partially supported by the European Commission via TMR network ‘Harmonic Analysis’, by Polish Grant from KBN 2 P03A 058 14, and by the Foundation for Polish Sciences, Subsidy 3/99.