Abstract We study pointwise convergence of the fractional Schrödinger means along sequences $t_{n}$ t n that converge to zero. Our main result is bounds on maximal function $\sup_{n} |e^{it_{n}(-\Delta )^{\alpha /2}} f| $ sup | <mml:msu...

We establish two results in the pointwise convergence problem of a trigonometric series [An] £ cne inl with lim Hm £ I bTck | = 0 |n|< -x. * Jn-»oo \k\-n for some nonnegative integer m. These results not only generalize Hardy's theorem, the Jordan test theorem and Fatou's theorem, but also complement the results on pointwise convergence of those Fourier series associated with known 1}-convergen...