Embedding Theorems And The Discreteness Of The Spectrum Of A Class Of Differential Opertors

In this paper, the embedding problem of weighted Sobolev spaces H_pⁿ which weight functions come from the coefficients of a defferential operator in weighted L_s spaces L_s,t with weight functions r(x) is investigated. Using the quardratic form comprasion methods and estimation for inequalities, we give conditions on these coeffients to ensure H_pⁿ to be continuously and compactly embedded in L_s. Then, on the relationship between the compactness of embedding operator and the discretness of the spectrum of self-adjoint operator, let p=s=2 and we obtain some criterions for the discrete spectrum of a class of 2n-order differential operators .