Title: Nikol'ski\uı, Jackson and Ul'yanov type inequalities with Muckenhoupt weights,
Abstract: In the present work we prove a Nikol'ski inequality for trigonometric
polynomials and Ul'yanov type inequalities for functions in Lebesgue spaces
with Muckenhoupt weights. Realization result and Jackson inequalities are
obtained. Simultaneous approximation by polynomials is considered. Some uniform
norm inequalities are transferred to weighted Lebesgue space.