Phuc Nguyen - On a conjecture of David R. Adams and related function spaces

We verify a conjecture of D. R. Adams on a capacitary strong type inequality that generalizes the classical capacitary strong type inequality of V. G. Maz'ya.

As a result, we characterize related function spaces as   K\"othe duals to a class of  Sobolev multiplier type spaces. The boundedness of the Hardy-Littlewood maximal function and the spherical maximal function on related Choquet spaces are also discussed.

This talk is based on joint work with Keng H. Ooi.