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Zap. Nauchn. Sem. POMI, 2014, Volume 424, Pages 210–234 (Mi znsl6016)  

This article is cited in 2 scientific papers (total in 2 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

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.

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English version:
Journal of Mathematical Sciences (New York), 2015, 209:5, 792–807

Bibliographic databases:

UDC: 517.5
Received: 18.06.2014

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://www.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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kislyakov S.V. Maksimov D.V. Stolyarov D.M., “Differential Expressions With Mixed Homogeneity and Spaces of Smooth Functions They Generate in Arbitrary Dimension”, J. Funct. Anal., 269:10 (2015), 3220–3263  crossref  mathscinet  zmath  isi  elib  scopus
    2. S. V. Kislyakov, D. V. Maksimov, “An embedding theorem with anisotropy for vector fields”, J. Math. Sci. (N. Y.), 234:3 (2018), 343–349  mathnet  crossref
  • Записки научных семинаров ПОМИ
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