Remarks, questions and conjectures on Landau-Kolmogorov-type inequalities

Results on Lanhu-Kolmogorov-type inequalities are surveyed with some new results given and some open questions raised. A multivariate analogue and analogues using different operators than the derivative are particularly emphasized. Equivalence between the periodic and nonperiodic case is shown. Failure of Kolmogorov's inequality for L-P spaces when 0 < p < 1 is demonstrated.