Abstract We consider fragmentation processes with values in the space of marked partitions $\mathbb{N}$ , i.e. where each block is decorated a nonnegative real number. Assuming that marks on distinct blocks evolve as independent positive self-similar Markov and determine speed at which their fragment, we get natural generalization fragmentations Bertoin ( Ann. Inst. H. Poincaré Prob. Statist. 3...

We prove that, after removing a zero Hausdorff dimension exceptional set of parameters, all self-similar measures on the line have power decay Fourier transform at infinity. In homogeneous case, when contraction ratios are equal, this is essentially due to Erdős and Kahane. non-homogeneous case difficulty we overcome apparent lack convolution structure.