In th is paper we consider two va riants of the Hankel tr ansform (they ar e called B essel-tr ans forma tions) which are de fined by: B (f) (y) ]1 fOO x 2 ]1 + 1 b (xy)f(x)dx o ]1 , foo 2 + 1 Y ]1 b (xy)f(x)dx o ]1 where b (z) = z-]1 J (z), J (z) b eing th e Bessel fu n ction of the ]1. ]1 ]1 first kind of order ]1. We extend th ese �r ansformations to cer­ ta in.spaces of generalized functions and prove several results on inversion , un iqueness, boundedness and analytic ity. The th eory

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... oped here is applied to solve certain Dirichl et problems .