No abstract

In this paper we consider the k‐plane Nikodym maximal estimates in the variable Lebesgue spaces Lp(·)false(Rnfalse). We first formulate the problem about the boundedness of the k‐plane Nikodym maximal and show that the maximal estimate in Lpfalse(Rnfalse) is equivalent to that in Lp(·)false(Rnfalse) for pfalse(·false)∈LH0∩N∞. So, the optimal Nikodym maximal estimate in Lp(·)false(R2false) follows from Cordoba's estimate.

We study averaged decay estimates for Fourier transforms of measures when the averages are taken over space curves with non-vanishing torsion. We extend the previously known results to higher dimensions and discuss sharpness of the estimates.2010 Mathematics Subject Classification. 42B10.