Erratum: Pointwise convergence of Fourier series


In the statements of Lemma 2, the main lemma, and the corollary to the main lemma, $\delta^{\frac{1}{2}-\eta}$ should be changed to $\delta^{\frac{1}{4}-\eta}$. Also, on pages 568 and 569, each $2^{-n(\frac{1}{2}-\eta)}$ should be changed to $2^{-n(\frac{1}{4}-\eta)}$. These changes are needed because, in the proof of Lemma 2, we pass to the adjoint before applying Lemma 1. Consequently, when the factor $\delta^{(1+\frac{1}{r})-5000\varepsilon}$ appears near the bottom of page 558, it ought to read $\delta^{(1-\frac{1}{r})-5000\varepsilon}$. Taking $r=2-\varepsilon$ and completing the proof of Lemma 2 as on page 559, we obtain the corrected form of Lemma 2. The other corrections indicated above came from applications of Lemma 2. Fortunately, these changes have no effect on the essential correctness of the paper.


Charles L. Fefferman