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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 424, Pages 210–234 (Mi znsl6016)  
This article is cited in 4 scientific papers (total in 4 papers)

Bilinear embedding theorems for differential operators in $\mathbb R^2$

D. M. Stolyarovab

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (315 kB) Citations (4)
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Abstract: We prove bilinear inequalities for differential operators in $\mathbb R^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However, here we study the phenomenon in itself. We consider elliptic case, where our analysis is complete, and non-elliptic, where it is not. The latter case is related to Strichartz estimates in a very easy case of two dimensions.
Key words and phrases: embedding theorems, bilinear operators, Strichartz estimates.
Received: 18.06.2014
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 209, Issue 5, Pages 792–807
DOI: https://doi.org/10.1007/s10958-015-2527-x
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: D. M. Stolyarov, “Bilinear embedding theorems for differential operators in $\mathbb R^2$”, Investigations on linear operators and function theory. Part 42, Zap. Nauchn. Sem. POMI, 424, POMI, St. Petersburg, 2014, 210–234; J. Math. Sci. (N. Y.), 209:5 (2015), 792–807
Citation in format AMSBIB
\Bibitem{Sto14}
\by D.~M.~Stolyarov
\paper Bilinear embedding theorems for differential operators in~$\mathbb R^2$
\inbook Investigations on linear operators and function theory. Part~42
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 424
\pages 210--234
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6016}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3481451}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 5
\pages 792--807
\crossref{https://doi.org/10.1007/s10958-015-2527-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84943453282}
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  • https://www.mathnet.ru/eng/znsl/v424/p210
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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