  We present the generalized parton distributions (GPDs) for the valence quarks
of the pion and the kaon in both momentum space and position space within the
basis light-front quantization framework. These GPDs are obtained from the
eigenvectors of a light-front effective Hamiltonian consisting of the
holographic quantum chromodynamics (QCD) confinement potential, a complementary
longitudinal confinement potential, and the color-singlet Nambu-Jona--Lasinio
interactions for the valence quarks of mesons. We then calculate the
generalized form factors of the pion and the kaon from the moments of these
GPDs. Combining the tensor form factors with the electromagnetic form factors,
we subsequently evaluate the impact parameter dependent probability density of
transversely polarized quarks inside the pion and the kaon. The numerical
results for the generalized form factors, tensor charges, as well as those for
the probability densities and the transverse shift of the polarized densities
are consistent with lattice QCD simulations and with chiral quark models.
