Phases of unimodular complex valued maps: optimal estimates, the factorization method, and the sum-intersection property of Sobolev spaces - Archive ouverte HAL Access content directly
Journal Articles Annales de l'Institut Henri Poincaré C, Analyse non linéaire Year : 2015

Phases of unimodular complex valued maps: optimal estimates, the factorization method, and the sum-intersection property of Sobolev spaces

Ioana Molnar
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Abstract

We establish optimal lifting estimates for unimodular complex valued maps in the Sobolev spaces $W^{s,p}$. This extends previous results of Bourgain, Dávila-Ignat and Merlet, and relies on new techniques (factorization, duality). We obtain a characterization, based on average martingale estimates, of fractional Sobolev spaces.
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Dates and versions

hal-00960317 , version 1 (18-03-2014)
hal-00960317 , version 2 (19-04-2014)

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  • HAL Id : hal-00960317 , version 2

Cite

Petru Mironescu, Ioana Molnar. Phases of unimodular complex valued maps: optimal estimates, the factorization method, and the sum-intersection property of Sobolev spaces. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2015, 32 (5), pp.965—1013. ⟨hal-00960317v2⟩
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