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Now, for x ∈ Ij fixed, we conclude that 1 B(x) sup I⊃Ij I I
1 + 2ξk −n−2 (δ1/3dj,l)nξndξ 1 + 2ξk −n−2 dξ 2k(2kδ1/3dj,l)n .
[C] L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135157.
[F] C. Fefferman, Pointwise convergence of Fourier series, Ann. of Math. 98 (1973), 551571.
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[S1] E.M. Stein, On limits of sequences of operators, Ann. of Math. 74 (1961), 140170.