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This article is cited in 13 scientific papers (total in 13 papers)
Norms of Dirichlet kernels and some other trigonometric polynomials in $L_p$-spaces
M. I. Dyachenko M. V. Lomonosov Moscow State University
Abstract:
The following problem is considered. Let
$\mathbf{a}=\{a_{\mathbf{n}}\}_{\mathbf{n}=1}^{\mathbf{M}}=\{a_{n_1,\dots,n_m}\}_{n_1,\dots,n_m=1}^{M_1,\dots,M_m}$
be a finite $m$-fold sequence of nonnegative numbers such that if $\mathbf{n}\ge\mathbf{k}$ then $a_{\mathbf{n}}\le a_{\mathbf{k}}$, and
$Q(\mathbf{x})=\sum_{\mathbf{n}=1}^{\mathbf{M}}a_{\mathbf{n}}e^{i\mathbf{nx}}$. The purpose of the work is to give best possible upper estimates of the norms $\|Q(\mathbf x)\|_p$ and $\|Q(\mathbf x)\|_{\mathbf{\delta},p}$ with $\boldsymbol\delta>0$ in terms of the coefficients $\{a_{\mathbf{n}}\}$. The Dirichlet kernels $D_U(\mathbf{x})=\sum_{\mathbf{n}\in U}e^{i\mathbf{nx}}$ with $U\in A_1$ present a particular case of $Q(\mathbf x)$.
Received: 23.01.1992
Citation:
M. I. Dyachenko, “Norms of Dirichlet kernels and some other trigonometric polynomials in $L_p$-spaces”, Mat. Sb., 184:3 (1993), 3–20; Russian Acad. Sci. Sb. Math., 78:2 (1994), 267–282
Linking options:
https://www.mathnet.ru/eng/sm969https://doi.org/10.1070/SM1994v078n02ABEH003469 https://www.mathnet.ru/eng/sm/v184/i3/p3
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Abstract page: | 502 | Russian version PDF: | 229 | English version PDF: | 31 | References: | 39 | First page: | 2 |
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