Paraproducts with flag singularities I. A case study.
C. Muscalu (2007)
Revista Matemática Iberoamericana
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C. Muscalu (2007)
Revista Matemática Iberoamericana
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P. Batchourine, C. Fefferman (2007)
Revista Matemática Iberoamericana
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Yahya Ould Hamidoune, Alain Plagne (2005)
Revista Matemática Iberoamericana
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Jong-Guk Bak, Daniel M. Oberlin, Andreas Seeger (2002)
Revista Matemática Iberoamericana
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Camil Muscalu, Jill Pipher, Terence Tao, Christoph Thiele (2006)
Revista Matemática Iberoamericana
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We prove that classical Coifman-Meyer theorem holds on any polidisc T or arbitrary dimension d ≥ 1.
f. bethuel, r. l. jerrard, d. smets (2008)
Revista Matemática Iberoamericana
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Philippe Laurençot, Stéphane Mischler (2002)
Revista Matemática Iberoamericana
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Lassi Päivärinta, Alexander Panchenko, Gunther Uhlmann (2003)
Revista Matemática Iberoamericana
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Giovanna Citti, Giuseppe Tomassini (2004)
Revista Matemática Iberoamericana
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Zoltán Buczolich (2005)
Revista Matemática Iberoamericana
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In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set G ⊂ R we construct a differentiable function f: G → R for which there exists an open set Ω ⊂ R such that ∇f(p) ∈ Ω for a p ∈ G but ∇f(q) ∉ Ω for almost every q ∈ G. This shows that the Denjoy-Clarkson property does not hold in higher dimensions.