Abstract:
It is proved that for any 0<ϵ<1 there exists a measurable set E⊂[0,1] with |E|>1−ϵ such that for any function f(x)∈L1[0,1] one can find a function g(x)∈L1[0,1] equal to f(x) on E such that its Fourier–Haar series converges absolutely in the metric of Lp(0,1), 0<p<1.
Key words and phrases:
Haar series, modification of functions, absolute convergece in the metric of Lp(0,1), 0<p<1.
Citation:
M. G. Grigoryan, “On the absolute convergence of Fourier–Haar series in the metric of Lp(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
\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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85075036841}
Linking options:
https://www.mathnet.ru/eng/znsl6565
https://www.mathnet.ru/eng/znsl/v467/p34
This publication is cited in the following 1 articles:
M. G. Grigoryan, “On unconditional and absolute convergence of the Haar series in the metric of Lp[0,1] with 0<p<1”, Siberian Math. J., 62:4 (2021), 607–615
Citation in format AMSBIB
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