Multidimensional Frank-Laptev-Weidl improvement of the Hardy inequality. (English) Zbl 07811759
Summary: We establish a new improvement of the classical \(L^p\)-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one-dimensional Hardy inequality. Using some radialisation techniques of functions and then exploiting symmetric decreasing rearrangement arguments on the real line, the new multidimensional version of the Hardy inequality is given. Some consequences are also discussed.
MSC:
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 35A23 | Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
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