A note on the Schrödinger smoothing effect

The Kato–Yajima smoothing estimate is a smoothing weighted L² estimate with a singular power weight for the Schrödinger propagator. The weight has been generalized relatively recently to Morrey–Campanato weights. In this paper we make this generalization more sharp in terms of the so‐called Kerman–Sawyer weights. Our result is based on a more sharpened Fourier restriction estimate in a weighted L² space. Obtained results are also extended to the fractional Schrödinger propagator.