Mathematical Notes

, Volume 70, Issue 5–6, pp 860–865

# Multidimensional Versions of Paley's Inequality

• V. A. Yudin
Article

## Abstract

For trigonometric polynomials of two variables whose spectrum lies both in the interior and on the boundary of a strictly convex domain, the lower bounds of their norms on % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca% WGmbaaaa!3934!$L$ are given. They are expressed in terms of the Fourier coefficients whose numbers are located on the boundary.

Paley's inequality trigonometric polynomial of two variables lower bounds for the norms of trigonometric polynomials $$n$$>n-dimensional torus lacunary sequence

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