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Zap. Nauchn. Sem. POMI, 2014, Volume 424, Pages 210–234
(Mi znsl6016)
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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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http://mi.mathnet.ru/eng/znsl6016 http://mi.mathnet.ru/eng/znsl/v424/p210
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:
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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
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S. V. Kislyakov, D. V. Maksimov, “An embedding theorem with anisotropy for vector fields”, J. Math. Sci. (N. Y.), 234:3 (2018), 343–349
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