POINTWISE BERNSTEIN-WALSH-TYPE INEQUALITIES IN REGIONS WITH CUSPS IN THE LEBESGUE SPACE

In this work, we investigate the order of growth of the modulus of an arbitrary algebraic polynomials in the weighted Lebesgue space, where the contour and the weight functions have some singularities. In particular, we obtain pointwise Bernstein-Walsh type estimation for algebraic polynomials in the unbounded regions with piecewise smooth boundary having exterior and interior zero angles.