Hardy and Hardy PDO Type Inequalities in Domains. Part 1

摘要

Here is given mainly an extensive treatment of Hardy inequalities in domains in211u001eR(N). Part II will continue on this theme and furthermore also treat Hardy PDO 211u001einequalities. The latter are Hardy inequalities involving Partial Differential 211u001eOperators instead of gradients in the inequalities. General subsets of the 211u001efunction space are also treated. Examples are nonnegative cones and are given a 211u001especial treatment. A part of the material is given in an encyclopedic fashion. 211u001eThis in order to get better overview and also be helpful in cases of outside 211u001eapplications. These papers are a continuation of (WAN5), which should be regarded 211u001ea prerequisite. Part II will contain more about Hardy inquealities and will treat 211u001eHardy PDO type inequalities in domains.