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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 243, Pages 96–103
(Mi tm423)
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This article is cited in 4 scientific papers (total in 4 papers)
Multiplicative Inequalities for Functions from the Hardy Space $H^1$ and Their Application to the Estimation of Exponential Sums
S. V. Bochkarev Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
Multiplicative inequalities are established for functions from the Hardy space $H^1$; based on these inequalities, lower estimates are found for the $L_1$-norm of a general exponential sum. Estimates for the $L_1$-norm of quadratic sums and sums with a power-law spectrum $\{n^h\}$, $h\ge 3$, are derived under certain conditions imposed on the absolute values of the coefficients in the sums. The estimates are sharp for $h\ge 3$.
Received in May 2003
Citation:
S. V. Bochkarev, “Multiplicative Inequalities for Functions from the Hardy Space $H^1$ and Their Application to the Estimation of Exponential Sums”, Function spaces, approximations, and differential equations, Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS, Trudy Mat. Inst. Steklova, 243, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 96–103; Proc. Steklov Inst. Math., 243 (2003), 89–97
Linking options:
https://www.mathnet.ru/eng/tm423 https://www.mathnet.ru/eng/tm/v243/p96
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