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We consider an impedance boundary‐value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a union of strips. Pseudo‐differential operators acting between Bessel potential spaces and Besov spaces are used to deal with this wave diffraction problem. In particular, these operators allow a reformulation of the problem into a system of integral equations. The main result presents impedance parameters which ensure the well‐posedness of the problem in scales of Bessel potential spaces and Besov spaces. First Published Online: 14 Oct 2010