Abstract
In a recent paper spaces of holomorphic functions on tubes in which generalize the Hardy H p spaces on tubes were defined and studied using the theory of ultra-distributions. Using L p theory of Fourier transforms Cauchy and Poisson integral representations of these functions were obtained and existence of S′(M k;M k)-boundary values of generalized H p-functions was established for 1 < p≤ 2. In this paper some of these results are extended to the case 2 < p < ∞. A Poisson integral representation is given and a sufficient condition for a function in the generalized space to be in H p-space is obtained in terms of its S′(M k;M k)-boundary value.
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