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A Seeger-Sogge-Stein theorem for bilinear Fourier integral operators
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 264, 1-54 p.Article in journal (Refereed) Published
Abstract [en]

We establish the regularity of bilinear Fourier integral operators with bilinear amplitudes in S-1,0(m) (n, 2) and non-degenerate phase functions, from L-P x L-q -> L-r under the assumptions that m <= -(n - 1)(vertical bar 1/p - 1/2 vertical bar + vertical bar 1/q - 1/2 vertical bar) and 1/p + 1/q = 1/r. This is a bilinear version of the classical theorem of Seeger-Sogge-Stein concerning the L-P boundedness of linear Fourier integral operators. Moreover, our result goes beyond the aforementioned theorem in that it also includes the case of quasi-Banach target spaces.

Place, publisher, year, edition, pages
2014. Vol. 264, 1-54 p.
Keyword [en]
Bilinear Fourier integral operators, Frequency space localisation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-234134DOI: 10.1016/j.aim.2014.07.009ISI: 000341615100001OAI: oai:DiVA.org:uu-234134DiVA: diva2:757808
Available from: 2014-10-23 Created: 2014-10-14 Last updated: 2017-12-05Bibliographically approved

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Rodriguez-Lopez, SalvadorStaubach, Wolfgang

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