Pointwise Convergence of Fourier Series

By J. A. D. Reyna. 2002

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Carleson's Theorem: Proof, Complements, Variations (2003, background): “e partial Fourier series of fconverges pointwise to f. This extends the result of P. Sj¨olin [88,89], who had the result above, but with a double log where there is a triple log above. Arias de Reyna [6,7] has noted an extension of this Theorem, in that one can deﬁne a rearrangement invariant Banach”
Weighted norm inequalities for maximally modulated singular integral operators (2005, background): “[ Ar ]). Recently [SS] have provided a general extrapolation principle that works for several maximal operators which, in particular, gives another proof of the aforementioned result of Antonov concerning S � and also yields some positive”