On the universal and strong (L1,L∞)-property related to Fourier–Walsh series

Martin G. Grigoryan

doi:10.1215/17358787-2017-0012

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Home > Journals > Banach J. Math. Anal. > Volume 11 > Issue 3 > Article

July 2017 On the universal and strong

(L^{1},L^{\infty})

-property related to Fourier–Walsh series

Martin G. Grigoryan

Banach J. Math. Anal. 11(3): 698-712 (July 2017). DOI: 10.1215/17358787-2017-0012

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Abstract

In this article, we construct a function $U\in L^{1}[0,1)$ with strictly decreasing Fourier–Walsh coefficients $\{c_{k}(U)\}\searrow$ , and having a universal and strong $(L^{1},L^{\infty})$ -property with respect to the Walsh system.

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Martin G. Grigoryan. "On the universal and strong $(L^{1},L^{\infty})$ -property related to Fourier–Walsh series." Banach J. Math. Anal. 11 (3) 698 - 712, July 2017. https://doi.org/10.1215/17358787-2017-0012