A variation norm Carleson theorem

@article{Oberlin2009AVN,
  title={A variation norm Carleson theorem},
  author={Richard Oberlin and Andreas Seeger and Terence Tao and Christoph Thiele and James Wright},
  journal={Journal of the European Mathematical Society},
  year={2009},
  volume={14},
  pages={421-464}
}
By a standard approximation argument it follows that S[f ] may be meaningfully defined as a continuous function in ξ for almost every x whenever f ∈ L and the a priori bound of the theorem continues to hold for such functions. Theorem 1.1 is intimately related to almost everywhere convergence of partial Fourier sums for functions in L[0, 1]. Via a transference principle [12], it is indeed equivalent to the celebrated theorem by Carleson [2] for p = 2 and the extension of Carleson’s theorem by… 
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