×

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.

MSC:

42B05 Fourier series and coefficients in several variables
42A55 Lacunary series of trigonometric and other functions; Riesz products
PDFBibTeX XMLCite
Full Text: DOI