Polynomials of least deviation from zero (Q5921707)

The author studies the problem of approximating a homogeneous polynomial of degree \(n\) on the unit disk \(B\), i.e., a polynomial of the form \[ F(x,y) = \sum_{k=0}^n a_k x^k y^{n-k}, \] by algebraic polynomials of smaller degree, i.e., polynomials of the form \[ P(x,y) = \sum_{k+\ell \leq n-1} x^k y^{\ell}. \] He obtains lower bounds for best approximation in the spaces \(L_p(B)\) for \(1 \leq p \leq \infty\).