A SHARPENED FORM of ADAMS TYPE INEQUALITIES on HIGHER ORDER SOBOLEV SPACES: A SIMPLE APPROACH

In this paper, we develop an extremely simple method to establish the sharpened Adams type inequalities on higher order Sobolev spaces Wm; n m (Rn) in the entire space Rn which can be stated as follows:(Equetions Presented).for any 0 << 1. Furthermore, we construct a proper test function sequence to derive the sharpness of the exponent of the above Adams inequalities. Namely, we will show that if 1, then the above supremum is in nite. Our argument avoids applying the complicated blow-up analysis often used in the literature to deal with such sharpened inequalities.