Weighted weak behaviour of Fourier-Jacobi series
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1
Universidad de La Rioja
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2
Universidad de Zaragoza
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ISSN: 0025-584X
Year of publication: 1992
Volume: 158
Issue: 1
Pages: 161-174
Type: Article
More publications in: Mathematische Nachrichten
Abstract
Mean convergence for series in Jacobi polynomials was first studied by Pollard in the 1940s, when he identified a critical index p, below which the mean convergence fails, and above which, up to the conjugate value, the mean convergence holds. The norm is the usual Lp norm with respect to the measure (1−x)α(1+x)β on (−1,1). When α,β>−1/2, the partial sum operator has been shown to be of restricted weak type at the critical index, but not of weak type. These results, which were proven by the authors, are extended to the case when α>−1/2, −1<β≤−1/2 and the case with α and β interchanged