On degree of approximation of the poisson means for f?l_{p}(??) functions at some smoothness points

The question "Given the Fourier transform of a Lebesgue integrable function f, how do we obtain f back again from its Fourier transform" was an important problem of Harmonic analysis and its applications, and it has drawn many famous matematicans' attentions. The Fourier transform of a Lebesgue integrable function may not be integrable therefore we could not obtain f back again by inverse Fourier transform of f. In order to get rid of this difficulty, matematicians reached different summability methods. The most well-known ones of these methods are Poisson, Gauss-Weierstrass and Riesz-Bochner. In this work we concentrate on some summability methods and we study Poisson means' convergence rate for f?L_{p}(??) functions at ?-smoothness points.