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Lebesgue Constants for Jacobi Expansions

Donald I. Cartwright
Proceedings of the American Mathematical Society
Vol. 87, No. 3 (Mar., 1983), pp. 427-433
DOI: 10.2307/2043625
Stable URL: http://www.jstor.org/stable/2043625
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Lebesgue Constants for Jacobi Expansions
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Abstract

Sharp estimates are given for the Lebesgue constants $|||s_n|||_p = \sup\{ \|s_nf\|_p: f \in L^p_w, \|f\|_p \leqslant 1\}$ for $p$ outside the Pollard interval $(p'_0, p_0)$, where $s_nf$ is the $n$th partial sum of the Jacobi expansion of a function $f$ which is in the $L^p$ space with respect to the weight $w(x) = (1 - x)^\alpha(1 + x)^\beta$ on $\lbrack -1, 1 \rbrack$.

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