Elliptic system Lyapunov inequality Radial functions Eigenvalue bounds p-Laplacian Embedding theorems P-Laplace operator Power weights Sobolev spaces 51M16 Bessel Boundary value problems Bounded domain Caffarelli-Kohn-Nirenberg inequalities Convolution Critical Sobolev exponent Critical growth Dirichlet boundary condition Eigenvalues bounds Fractional Laplace operator Fractional integrals Fractional integration Fractional-order Sobolev spaces Harmonic oscillator Heat semigroups of operators Hermite expansions Laguerre Laguerre expansions Laplace equation Laplace transforms