On Wirtinger's inequality and its elementary proof

By an elementary method, we exactly determine the best possible constant and its attaining function which satisfy ‖f ‖q Cq‖f ′‖q (1 < q < ∞) for certain class of continuously differentiable functions on the unit interval [0, 1] . Mathematics subject classification (2000): 26D15, 60E15, 47B15.