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An integral equation of the first kind of convolution type is considered. A method closely related to Tikhonov regularization is used for constructing regularized approximate solutions that under certain assumptions converge to the exact solution of this ill-posed problem. V I Burenkov, I F Dorofeev and A S Pankratov obtained solutions of this problem for the isotropic case by using Nikol'skiĭ-Besov spaces of functions possessing some common smoothness of fractional order as a means of characterizing the smoothness properties of the exact solution and the error on the right-hand side. The main aim of the present work is to obtain similar results for the anisotropic case, thus allowing the right-hand side error, the exact and regularized solutions to be considered as members of a wider class of functions than in the former case. A complete investigation of the anisotropic case is carried out. Some of the results obtained are also new for the isotropic case. [ABSTRACT FROM AUTHOR]