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

Abstract

The Poisson summation formula for Hardy spaces $$H^p\left( T_\Gamma \right) $$ in tubes $$T_\Gamma \subset \mathbb {C}^n$$ for $$p\in \left( 0,1\right] $$ is obtained. Unlike the case of $$L^p\left( \mathbb {R}^n\right) $$ spaces, the formula holds everywhere in $$T_\Gamma $$ 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.