Geodesic
Pointwise convergence of Fourier series (I). On a conjecture of Konyagin
Journal of the European Mathematical Society, Tome 19 (2017) no. 6, pp. 1655-1728

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We provide a near-complete classification of the Lorentz spaces Λφ​ for which the sequence {Sn​}n∈N​ of partial Fourier sums is almost everywhere convergent along lacunary subsequences. Moreover, under mild assumptions on the fundamental function φ, we identify Λφ​:=L log log L log log log log L as the largest Lorentz space on which the lacunary Carleson operator is bounded as a map to L1,∞. As a consequence, we
DOI : 10.4171/jems/703
Classification : 42-XX, 46-XX
Keywords: Time-frequency analysis, Carleson's Theorem, lacunary subsequences, pointwise convergence 
@article{JEMS_2017_19_6_a1,
     author = {Victor Lie},
     title = {Pointwise convergence of {Fourier} series {(I).} {On} a conjecture of {Konyagin}},
     journal = {Journal of the European Mathematical Society},
     pages = {1655--1728},
     publisher = {mathdoc},
     volume = {19},
     number = {6},
     year = {2017},
     doi = {10.4171/jems/703},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/703/}
}
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Victor Lie. Pointwise convergence of Fourier series (I). On a conjecture of Konyagin. Journal of the European Mathematical Society, Tome 19 (2017) no. 6, pp. 1655-1728. doi: 10.4171/jems/703

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