On the pointwise ergodic theorem on \(L^ p\) for arithmetic sets (Q1101569)

In this paper the author extends the according pointwise ergodic theorem for \(L^ 2\)-functions of the paper above to the case \(p>(\sqrt{5+1})/2\), i.e. \(\frac{1}{N}\sum_{n<N}T^{p(n)}f\) converges almost surely for any \(f\in L^ p(X,\mu)\) (p(n) a polynomial with integer coefficients). The method is based on interpolation and the results of the first part. In order to make the proof not too complicated ``only'' the case of \(p(n)=n^ t\) is explicitely proved.