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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 456, Pages 25–36 (Mi znsl6419)  

This article is cited in 6 scientific papers (total in 6 papers)

$K$-closedness for weighted Hardy spaces on the torus $\mathbb T^2$

V. A. Borovitskiyab

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (218 kB) Citations (6)
References:
Abstract: Certain sufficient conditions are established for the couple of weighted Hardy spaces $(H_r(w_1(\cdot,\cdot)),H_s(w_2(\cdot,\cdot)))$ on the two-dimensional torus $\mathbb T^2$ to be $K$-closed in the couple $(L_r(w_1(\cdot,\cdot)),L_s(w_2(\cdot,\cdot)))$. For $0<r<s<1$ the condition $w_1,w_2\in A_\infty$ suffices ($A_\infty$ is the Muckenhoupt condition over rectangles). For $0<r<1<s<\infty$ it suffices that $w_1\in A_\infty$, $w_2\in A_s$. For $1<r<s=\infty$, we assume that the weights are of the form $w_i(z_1,z_2)=a_i(z_1)u_i(z_1,z_2)b_i(z_2)$, and then the following conditions suffice: $u_1\in A_p$, $u_2\in A_1$, $u_2^pu_1\in A_\infty$, $\log a_i,\log b_i\in BMO$. The last statement generalizes the previously known result for the case of $u_i\equiv1$, $i=1,2$. Finally, for $r=1$, $s=\infty$, the conditions $w_1,w_2\in A_1$, $w_1w_2\in A_\infty$ suffice.
Key words and phrases: Hardy classes, $K$-closedness, the space BMO, Muckenhoupt conditions.
Received: 05.06.2017
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 234, Issue 3, Pages 282–289
DOI: https://doi.org/10.1007/s10958-018-4004-9
Document Type: Article
UDC: 517.5
Language: Russian
Citation: V. A. Borovitskiy, “$K$-closedness for weighted Hardy spaces on the torus $\mathbb T^2$”, Investigations on linear operators and function theory. Part 45, Zap. Nauchn. Sem. POMI, 456, POMI, St. Petersburg, 2017, 25–36; J. Math. Sci. (N. Y.), 234:3 (2018), 282–289
Citation in format AMSBIB
\Bibitem{Bor17}
\by V.~A.~Borovitskiy
\paper $K$-closedness for weighted Hardy spaces on the torus~$\mathbb T^2$
\inbook Investigations on linear operators and function theory. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 456
\pages 25--36
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6419}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 234
\issue 3
\pages 282--289
\crossref{https://doi.org/10.1007/s10958-018-4004-9}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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