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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 243, Pages 96–103 (Mi tm423)  
This article is cited in 4 scientific papers (total in 4 papers)

Multiplicative Inequalities for Functions from the Hardy Space H1 and Their Application to the Estimation of Exponential Sums

S. V. Bochkarev

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (165 kB) Citations (4)
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Abstract: Multiplicative inequalities are established for functions from the Hardy space H1; based on these inequalities, lower estimates are found for the L1-norm of a general exponential sum. Estimates for the L1-norm of quadratic sums and sums with a power-law spectrum {nh}, h⩾3, are derived under certain conditions imposed on the absolute values of the coefficients in the sums. The estimates are sharp for h⩾3.
Received in May 2003
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. V. Bochkarev, “Multiplicative Inequalities for Functions from the Hardy Space H1 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
Citation in format AMSBIB
\Bibitem{Boc03}
\by S.~V.~Bochkarev
\paper Multiplicative Inequalities for Functions from the Hardy Space~$H^1$ and Their Application to the Estimation of Exponential Sums
\inbook Function spaces, approximations, and differential equations
\bookinfo Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS
\serial Trudy Mat. Inst. Steklova
\yr 2003
\vol 243
\pages 96--103
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm423}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2049465}
\zmath{https://zbmath.org/?q=an:1068.42019}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2003
\vol 243
\pages 89--97
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  • https://www.mathnet.ru/eng/tm423
  • https://www.mathnet.ru/eng/tm/v243/p96
    • This publication is cited in the following 4 articles:
    1. S. V. Bochkarev, “de la Vallée-Poussin means of Fourier series for the quadratic spectrum and for spectra with power-like density”, Russian Math. Surveys, 69:1 (2014), 119–152  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64  mathnet  crossref  mathscinet  elib
    3. S. V. Bochkarev, “New Inequalities in the Littlewood–Paley Theory and Estimates of the $L_1$ Norm of Trigonometric Series and Polynomials”, Proc. Steklov Inst. Math., 248 (2005), 59–68  mathnet  mathscinet  zmath
    4. Bochkarev S.V., “New multiplicative inequalities and estimates for the $L_1$-norms of trigonometric series and polynomials”, Dokl. Math., 72:2 (2005), 762  mathnet  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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