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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 456, Pages 37–54 (Mi znsl6420)  
This article is cited in 1 scientific paper (total in 1 paper)

On an equivalent norm on $\mathrm{BMO}$

I. Vasilyevab, A. Tselishchevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Chebyshev Laboratory, St. Petersburg State University, St. Petersburg, Russia
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Abstract: We extand the inequality proved by S. V. Bochkarev to a larger class of convolution operators, assuming that the Fourier transforms of the kernels of these operators satisfy certain conditions in the spirit of the Hörmander–Mikhlin multiplier theorem. Therefore, we give a new characterization of $\mathrm{BMO}$.
Key words and phrases: $\mathrm{BMO}$ space, Hörmander–Mikhlin multiplier theorem.
Funding agency Grant number
Russian Science Foundation 14-21-00035
Received: 17.07.2017
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 234, Issue 3, Pages 290–302
DOI: https://doi.org/10.1007/s10958-018-4005-8
Document Type: Article
UDC: 517.5
Language: Russian
Citation: I. Vasilyev, A. Tselishchev, “On an equivalent norm on $\mathrm{BMO}$”, Investigations on linear operators and function theory. Part 45, Zap. Nauchn. Sem. POMI, 456, POMI, St. Petersburg, 2017, 37–54; J. Math. Sci. (N. Y.), 234:3 (2018), 290–302
Citation in format AMSBIB
\Bibitem{VasTse17}
\by I.~Vasilyev, A.~Tselishchev
\paper On an equivalent norm on~$\mathrm{BMO}$
\inbook Investigations on linear operators and function theory. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 456
\pages 37--54
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6420}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 234
\issue 3
\pages 290--302
\crossref{https://doi.org/10.1007/s10958-018-4005-8}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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