Abstract
AbstractLet 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 Sn are uniformly bounded from Lp,1 to Lp,∞, 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→uSn(u−1f), where u is also Jacobi weight.
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