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In this paper, we develop Terence Tao's harmonic analysis method and apply itto restricted sumsets. The well known Cauchy-Davenport theorem asserts that if$A$ and $B$ are nonempty subsets of $Z/pZ$ with $p$ a prime, then $|A+B|\gemin{p,|A|+|B|-1}$, where $A+B={a+b: a\in A, b\in B}$. In 2005, Terence Tao gavea harmonic analysis proof of the Cauchy-Davenport theorem, by applying a newform of the uncertainty principle on Fourier transform. We modify Tao's methodso that it can be used to prove the following extension of the Erdos-Heilbronnconjecture: If $A,B,S$ are nonempty subsets of $Z/pZ$ with $p$ a prime, then$|{a+b: a\in A, b\in B, a-b not\in S}|\ge min {p,|A|+|B|-2|S|-1}$.

A variant of Tao's method with application to restricted sumsets