A Sharp Inequality of J. Moser for Higher Order Derivatives

In fact go = nwl/(1), where wnis the area of the surface of the unit n-ball. Also, he notes that if /3 exceeds go then (1) can no longer hold with some co independent of the u, satisfying (2). The fact that this result holds for some /3 > 0 independent of u has been observed now by several authors with a variety of proofs; see [24], [20], [23], [22], [10], [4], [1], [2], [13], [14], for example. The earliest of these arguments expands the exponential function in a power series. Then observing that the norm in the imbedding