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Weighted Weak Behaviour of Fourier-Jacobi Series

✍ Scribed by José J. Guadalupe; Mario Pérez; Juan L. Varona


Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
503 KB
Volume
158
Category
Article
ISSN
0025-584X

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✦ Synopsis


Abstract

Let w(x) = (1 ‐ x)^α^ (1 + x)^β^ be a Jacobi weight on the interval [‐1, 1] and 1 < p < ∞. If either α > −1/2 or β > −1/2 and p is an endpoint of the interval of mean convergence of the associated Fourier‐Jacobi series, we show that the partial sum operators S~n~ are uniformly bounded from L^p,1^ to L^p,∞^, thus extending a previous result for the case that both α, β > −1/2. For α, β > −1/2, we study the weak and restricted weak (p, p)‐type of the weighted operators f→uS~n~(u^−1^f), where u is also Jacobi weight.


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