Ushangi Goginava, Károly Nagy, "Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series", Journal of Function Spaces, vol. 8, Article ID 638327, 20 pages, 2010. https://doi.org/10.1155/2010/638327
Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series
The main aim of this paper is to prove that there exists a martingale f∈ H1/2 such that the maximal Fejér operator with respect to Walsh-Kaczmarz system does not belong to the space L1/2. For the two-dimensional case, we prove that there exists a martingale such that the restricted (unrestricted) maximal operator of Fejér means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-L1/2.
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