# 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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