Estimates of norms of eigenfunctions of the Sturm-Liouville problem in Sobolev spaces
The eigenfunctions of the Sturm-Liouville problem with Dirichlet boundary conditions on \([0,1]\) for the equation \(-y''+q(x)y=\lambda\rho(x)y\), \(q\in L_{1}(0,1)\), \(0<m<\rho(x)<M<\infty\), are studied. It is assumed that the eigenfunctions are normed in \(L_{q}((0,1);\rho(x))\), \(q\geq1\). Their norms in the Sobolev spaces \(W_{p}^{\theta}\), \(p\geq1\), \(0\leq\theta\leq2\), are estimated.
scientific article; zbMATH DE number 2115603