In this talk, we are concerned with the uniform Sobolev inequalities on the d- torus, which were obtained by Shen [S] and Shen-Zhao [SZ]. The uniform Sobolev inequalities on the d-torus have been studied to observe absolute continuity of periodic operators. I rst review the absolute continuity of the periodic Schrodinger operators and discuss how to derive the absolute continuity from the uniform Sobolev inequality. After that, I sketch the proof of Shen and Zhao for the uniform Sobolev inequalities by using multiplier approach.