Bounds on the Pion Electromagnetic Form Factor

Upper and lower bounds for the spacelike pion form factor are given in terms of a dispersion integral of the modulus of its timelike form factor. Similar bounds are obtained for its phase (in the timelike region) which in turn provide information on the low-energy $P$-wave pion-pion scattering. The upper and lower bounds approach the same limit, and hence become equalities, if the zeros of the form factor are far from the physical region of interest.