We study the error performances of p -norm Support Vector Machine classifiers based on reproducing kernel Hilbert spaces. We focus on two category problem and choose the data-dependent polynomial kernels as the Mercer kernel to improve the approximation error. We also provide the standard estimation of the sample error, and derive the explicit learning rate. Index Terms-Support vector machine classification; Learning rate; Reproducing kernel Hilbert spaces; Cesaro means. [ ( ( )) ( )] [ ( ( )) ( )]