On L_p-error of bivariate polynomial interpolation on the square

We obtain estimates of the L_p-error of the bivariate polynomial interpolation on the Lissajous–Chebyshev node points for wide classes of functions including non-smooth functions of bounded variation in the sense of Hardy–Krause. The results show that L_p-errors of polynomial interpolation on the Lissajous–Chebyshev nodes have almost the same behavior as the polynomial interpolation in the case of the tensor product Chebyshev grid.