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We present the systematical decomposition results of three-dimensional (3D)fragmentation functions (FFs) from parton correlators for spin-1 hadron. Wechoose one of the best process $e^+e^-\to V\pi X$ to study the 3D and tensorpolarization dependent FFs. By making a general kinematic analysis we show thatthe cross section is expressed by 81 independent structure functions, and getthe results of the azimuthal and spin asymmetries. We also present the partonmodel results for this process and express the results in terms of the 3D FFs.Based on this formalism, we also give the numerical results of hadronlongitudinal polarizations and predict the energy dependence.

Azimuthal and spin asymmetries in $e^+e^-\to V \pi X$ at high energies and 3D fragmentation functions