Abstract
The paper addresses questions on existence and structure of universal functions for spaces L1(E), E ⊂ [0, 1)2, with respect to the doubleWalsh system in the sense of signs of Fourier coefficients. It is shown that for each ε > 0 one can find a measurable set Eε ⊂ [0, 1)2 with measure |Eε| > 1−ε, such that by a proper modification of any integrable function f ∈ L1[0, 1)2 outside Eε one can get an integrable function f̃ ∈ L1[0, 1)2 which is universal for L1(Eε) with respect to the double Walsh system in the sense of signs of Fourier coefficients.
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Grigoryan’s work was partially supported by the RA MES (Republic of Armenia, Ministry of Education and Science) State Committee of Science, in the frame of the research project 18T-1A148.
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Sargsyan, A., Grigoryan, M. Universal functions with respect to the double Walsh system for classes of integrable functions. Anal Math 46, 367–392 (2020). https://doi.org/10.1007/s10476-020-0024-z
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DOI: https://doi.org/10.1007/s10476-020-0024-z