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We prove the regularity of weak 1/2-harmonic maps  from the real line into a sphere. The key point in our result is first   a formulation of the 1/2-harmonic map equation in the form of  a non-local  linear Schr\"odinger type equation  with a   3-terms commutators in the right-hand-side . We then establish a sharp estimate for these  3-commutators

Three-term commutator estimates and the regularity of ∖half∖-harmonic maps into spheres