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Zap. Nauchn. Sem. POMI, 2018, Volume 467, Pages 34–54 (Mi znsl6565)  

On the absolute convergence of Fourier–Haar series in the metric of $L^p(0,1)$, $0<p<1$

M. G. Grigoryan

Faculty of Physics, Yerevan State University, Yerevan, Armenia

Abstract: It is proved that for any $0<\epsilon<1$ there exists a measurable set $E\subset[0,1]$ with $|E|>1-\epsilon$ such that for any function $f(x)\in L^1[0,1]$ one can find a function $g(x)\in L^1[0,1]$ equal to $f(x)$ on $E$ such that its Fourier–Haar series converges absolutely in the metric of $L^p(0,1)$, $0<p<1$.

Key words and phrases: Haar series, modification of functions, absolute convergece in the metric of $L^p(0,1)$, $0<p<1$.

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English version:
Journal of Mathematical Sciences (New York), 2019, 243:6, 844–858

UDC: 517.518
Received: 08.06.2018

Citation: M. G. Grigoryan, “On the absolute convergence of Fourier–Haar series in the metric of $L^p(0,1)$, $0<p<1$”, Investigations on linear operators and function theory. Part 46, Zap. Nauchn. Sem. POMI, 467, POMI, St. Petersburg, 2018, 34–54; J. Math. Sci. (N. Y.), 243:6 (2019), 844–858

Citation in format AMSBIB
\Bibitem{Gri18}
\by M.~G.~Grigoryan
\paper On the absolute convergence of Fourier--Haar series in the metric of $L^p(0,1)$, $0<p<1$
\inbook Investigations on linear operators and function theory. Part~46
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 467
\pages 34--54
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6565}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 243
\issue 6
\pages 844--858
\crossref{https://doi.org/10.1007/s10958-019-04584-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85075036841}


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