Some Landau-Kolmogorov Type Inequalities For Differential Operators Generated By Polynomials

In this paper, we establish some Landau-Kolmogorov type inequalities for differential operators generated by polynomials in the following formparallel to P(D)f parallel to(p) <= K-1(epsilon, P)parallel to f parallel to(q) + K-2(epsilon, m)parallel to D-m(P(D)f)parallel to(p)for all epsilon > 0, where 0 < q <= p <= infinity, and the differential operator P(D) is obtained from the polynomial P(x) by substituting x -> i partial derivative/partial derivative x. Moreover, the explicit form of K-1(epsilon, P) and K-2(epsilon, m) are given.