Wiener Type Theorems for Jacobi Series with Nonnegative Coefficients
نویسنده
چکیده
This paper gives three theorems regarding functions integrable on [−1, 1] with respect to Jacobi weights, and having nonnegative coefficients in their (Fourier–)Jacobi expansions. We show that the L-integrability (with respect to the Jacobi weight) on an interval near 1 implies the L-integrability on the whole interval if p is an even integer. The Jacobi expansion of a function locally in L∞ near 1 is shown to converge uniformly and absolutely on [−1, 1]; in particular, such a function is shown to be continuous on [−1, 1]. Similar results are obtained for functions in local Besov approximation spaces.
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