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Zap. Nauchn. Sem. POMI, 2013, Volume 416, Pages 59–69 (Mi znsl5703)  

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

The property $\log(f)\in BMO(\mathbb R^n)$ in terms of the Riesz transformations

I. M. Vasilyev

St. Petersburg State University, St. Petersburg, Russia

Abstract: The condition mentioned in the title is equivalent to the representability of $f$ as a quotient $f=v_1/v_2$ where $v_1$ and $v_2$ obey the inequality $|R_jv_i|\le cv_i$, $i=1,2$, $j=1,\ldots,n$. Here $R_1,\ldots,R_n$ are the Riesz transformations.

Key words and phrases: Riesz transformation, subharmonicity, reverse Hölder inequality.

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English version:
Journal of Mathematical Sciences (New York), 2014, 202:4, 519–525

UDC: 517.5
Received: 24.02.2013

Citation: I. M. Vasilyev, “The property $\log(f)\in BMO(\mathbb R^n)$ in terms of the Riesz transformations”, Investigations on linear operators and function theory. Part 41, Zap. Nauchn. Sem. POMI, 416, POMI, St. Petersburg, 2013, 59–69; J. Math. Sci. (N. Y.), 202:4 (2014), 519–525

Citation in format AMSBIB
\Bibitem{Vas13}
\by I.~M.~Vasilyev
\paper The property $\log(f)\in BMO(\mathbb R^n)$ in terms of the Riesz transformations
\inbook Investigations on linear operators and function theory. Part~41
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 416
\pages 59--69
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5703}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 202
\issue 4
\pages 519--525
\crossref{https://doi.org/10.1007/s10958-014-2058-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84922072928}


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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. D. V. Rutsky, “$\mathrm A_1$-regularity and boundedness of Riesz transforms in Banach lattices of measurable functions”, J. Math. Sci. (N. Y.), 229:5 (2018), 561–567  mathnet  crossref  mathscinet
    2. Lerner A.K., “A Note on the Coifman-Fefferman and Fefferman-Stein Inequalities”, Ark. Mat., 58:2 (2020), 357–367  crossref  mathscinet  zmath  isi
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