In order to evaluate the goodness of frequency hopping sequence design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen frequency hopping sequence, so the study of the partial Hamming correlation of frequency hopping sequence is particularly important. In this paper, the maximum partial Hamming correlation lower bounds of frequency hopping sequences with low hit zone, with respect to the size of the frequency slot set, the length of correlation window, the family size, the low hit zone, the maximum partial Hamming autocorrelation and the maximum partial Hamming crosscorrelation are established. It is shown that the new bounds include the known Lempel-Greenberger bound, Peng-Fan bounds, Eun-Jin-Hong-Song bound and Peng-Fan-Lee bounds as special cases.