A logarithmic extension of the Hölder inequality (Q1304738)

This paper is based on a classic generalization due to Hardy, Littlewood and Pólya of the Hölder inequality on a probability space. The authors establish a logarithmic extension of this result and their study is motivated by the problem of strict localization of \(L^2\) and related estimates for the Ginzburg-Landau system \(u_t=\lambda u+(1+i\nu)\Delta u-(1+i\mu)ug(|u|^2)\), in the case where the nonlinearity \(g(\rho)\) behaves as \((\log \rho)^\beta\) for large \(\rho\).