On an oppenheim-type conjecture for systems of quadratic forms |
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| Authors: | Alexander Gorodnik |
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| Institution: | (1) Department of Mathematics and Statistics, University of Edinburgh James Clerk Maxwell Building, Edinburgh EH9 3JZ Scotland, U.K.;(2) Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Ciudad Universitaria de Canto Blanco, 28049 Madrid, Spain |
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| Abstract: | In this paper we establish dimension freeL
p
(ℝ
n
,|x|α) norm inequalities (1<p<∞) for the oscillation and variation of the Riesz transforms in ℝ
n
. In doing so we findA
p
-weighted norm inequalities for the oscillation and the variation of the Hilbert transform in ℝ. Some weighted transference
results are also proved.
Partially supported by European Commission via the TMR network “Harmonic Analysis”. |
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| Keywords: | |
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