Sharp inequalities between \(L^p\)-norms for the higher dimensional Hardy operator and its dual. (English) Zbl 1473.43001
Summary: We derive the two-sided inequalities between \(L^p(X)\)-norms \((1<p<\infty)\) of the higher dimensional Hardy operator and its dual, where the underlying space \(X\) is the Heisenberg group \(\mathbb{H}^n\) or the Euclidean space \(\mathbb{R}^n\). The interest of main results is that it relates two-sided inequalities with sharp constants which are dimension free. The methodology is completely depending on the rotation method.
MSC:
| 43A15 | \(L^p\)-spaces and other function spaces on groups, semigroups, etc. |
| 26D15 | Inequalities for sums, series and integrals |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
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