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The Fourier-Laplace transforms on Rn (n > 2) whose images belong to the Bergman spaces are investigated from the point of view of a general theory of integral transforms. The central problems are to give the expressions of the Bergman kernels in terms of the Fourier-Laplace transforms, and to investigate the relationship between the domains and the ranges in the expressions.doi:10.2307/2047346 fatcat:7c5zhddfhjeddanm7jwefz66fu