Estimates for eigenvalues of fourth-order weighted polynomial operator

In this paper,we investigate the Dirichlet eigenvalue problem of fourth-order weighted polynomial operator △~2u-a△u+bu=Λρu,inΩR~n,u|Ω=uvΩ=0,where the constants a,b≥0.We obtain some estimates for the upper bounds of the (k+1)-th eigenvalueΛ_k+1 in terms of the first k eigenvalues.Moreover,these results contain some results for the biharmonic operator.     

Generalized composition operators from F(p, q, s) spaces to Bloch-type spaces

Let H(B) denote the space of all holomorphic functions on the unit ball B of Cⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. In this paper, we investigate the boundedness and compactness of the generalized composition operator

     

Tauberian theorems for double sequences that are statistically summable (C,1,1)

Let be a double sequence of real or complex numbers, and set