The helical transform and the a.e. convergence of Fourier series (Q1320942)

In this paper the authors prove that the boundedness for the following operators acting on \(L\) for \(1<p<\infty\) are equivalent: 1) Partial sums of Fourier series. 2) Maximal helical transform on \(l^ p\). 3) Double maximal helical transform on \(l^ p\). 4) Double maximal helical transform on \(L^ p\). 5) Double maximal estimate for the ergodic Fejér sum. 6) Double maximal estimate for a measure preserving flow. 7) Carlson-Hunt estimate. The author goes on to further refine estimates of constants and prove certain equivalences.