PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On the existence of universal functions with respect to the double Walsh system for classes of integrable functions

Volume 161 / 2020

Artsrun Sargsyan Colloquium Mathematicum 161 (2020), 111-129 MSC: Primary 42C10; Secondary 43A15. DOI: 10.4064/cm7759-4-2019 Published online: 5 March 2020


It is shown that there exists a function $U\in L^1([0,1)^2)$ such that for each $\varepsilon \gt 0$ one can find a measurable set $E_\varepsilon \subset [0,1)^2$ with $|E_\varepsilon | \gt 1-\varepsilon $ such that $U$ is universal for the space $L^{1}(E_\varepsilon )$ with respect to the double Walsh system $\{W_k(x) W_s(y)\}$ in the sense of signs of Fourier coefficients, i.e. any function $f\in L^1 (E_\varepsilon )$ is a limit (over rectangles and over spheres) of $\sum \delta _{k,s} a_{k,s}(U)W_k (x)W_s (y)$ for some signs $\delta _{k,s}=\pm 1$, where $a_{k,s}(U)$ are the Fourier–Walsh coefficients of $U$.


  • Artsrun SargsyanRussian-Armenian University
    Hovsep Emin 123
    0051 Yerevan, Armenia

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image