Nikol'skii inequalities for Lorentz spaces (Q968581)

A general approach is presented to establish Nikol'skii type inequalities for various Lorentz spaces. The key ingredient for the proof is either a Bernstein type inequality or a Remez-type inequality. Applications of the results to trigonometric polynomials on the torus \(T^d\), algebraic polynomials on \([-1,1]\), spherical harmonic polynomials on the unit sphere \(S^{d-1}\) in \(\mathbb{R}^d\), algebraic polynomial on \(\mathbb{R}\) with Freud's weights and others are presented.