Poisson Summation Formula in Hardy Spaces Hp(TΓ)H^p(T_\Gamma ) H p ( T Γ ) , p∈(0,1]p\in (0,1] p ∈ ( 0 , 1 ]

The Poisson summation formula for Hardy spaces Hp(TΓ) in tubes TΓ⊂ Cn for p∈ (0 , 1 ] is obtained. Unlike the case of Lp(Rn) spaces, the formula holds everywhere in TΓ without any additional assumptions. To the best of our knowledge, the result is new even for the univariate case—Hardy spaces in the upper half-plane