Universal functions for classes \[L^p[0,1)^2\] , \[p\in (0,1)\] , with respect to the double Walsh system

Universal functions for classes \[L^p[0,1)^2\] , \[p\in (0,1)\] , with respect to the double Walsh system

In the paper it is shown that there exists a function \[U\in L^1[0,1)^2\], which is universal for all class \[L^{p}[0,1)^2\], \[p\in (0,1)\], by rectangles and by spheres with respect to the double Walsh system in the sense of signs of Fourier coefficients.

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2019-11, Vol.23 (5), p.1261-1280
Hauptverfasser: Sargsyan, Artsrun, Grigoryan, Martin
Format: Artikel
Sprache:eng
Schlagworte:
Rectangles
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Zusammenfassung:In the paper it is shown that there exists a function \[U\in L^1[0,1)^2\], which is universal for all class \[L^{p}[0,1)^2\], \[p\in (0,1)\], by rectangles and by spheres with respect to the double Walsh system in the sense of signs of Fourier coefficients.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-019-00663-7