Yudin, V. A. Multidimensional versions of Paley’s inequality. (English. Russian original) Zbl 1022.42006 Math. Notes 70, No. 6, 860-865 (2001); translation from Mat. Zametki 70, No. 6, 941-947 (2001). Summary: For trigonometric polynomials of two variables whose spectra ly both in the interior and on the boundary of a strictly convex domain, the lower bounds of their norms on \(L_1\) are given. They are expressed in terms of the Fourier coefficients whose numbers are located on the boundary. Cited in 1 Document MSC: 42B05 Fourier series and coefficients in several variables 42A55 Lacunary series of trigonometric and other functions; Riesz products Keywords:Paley’s inequality; lacunary sequence; trigonometric polynomials of two variables; lower bounds; norms; Fourier coefficients PDFBibTeX XMLCite \textit{V. A. Yudin}, Math. Notes 70, No. 6, 860--865 (2001; Zbl 1022.42006); translation from Mat. Zametki 70, No. 6, 941--947 (2001) Full Text: DOI