We prove a weak-Lp bound for the Walsh-Carleson operator for p near 1, improving on a theorem of Sjölin. We relate our result to the conjectures that the Walsh-Fourier and Fourier series of a function f∈LlogL(T) converge for almost every x∈T. © 2014 Académie des sciences.
Weak-Lp bounds for the Carleson and Walsh-Carleson operators / Di Plinio, F.. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 352:4(2014), pp. 327-331. [10.1016/j.crma.2014.02.005]
Weak-Lp bounds for the Carleson and Walsh-Carleson operators
Di Plinio F.
2014
Abstract
We prove a weak-Lp bound for the Walsh-Carleson operator for p near 1, improving on a theorem of Sjölin. We relate our result to the conjectures that the Walsh-Fourier and Fourier series of a function f∈LlogL(T) converge for almost every x∈T. © 2014 Académie des sciences.File in questo prodotto:
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