تقرير
When are the Hardy-Littlewood inequalities contractive?
| العنوان: | When are the Hardy-Littlewood inequalities contractive? |
|---|---|
| المؤلفون: | Cavalcante, W. V., Nogueira, T., Pellegrino, D. M., Santos, J., Rueda, P. |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis |
| الوصف: | The optimal constants of the $m$-linear Bohnenblust-Hille and Hardy-Littlewood inequalities are still not known despite its importance in several fields of Mathematics. For the Bohnenblust-Hille inequality and real scalars it is well-known that the optimal constants are not contractive. In this note, among other results, we show that if we consider sums over $M:=M(m)$ indexes with $M\log M=o(m)$, the optimal constants are contractive. For instance, we can consider% \[ M=\left\lfloor \frac{m}{\left( \log m\right) ^{1+\frac{1}{\log\log\log m}}% }\right\rfloor \] where $\lfloor x\rfloor:=\max\{n\in\mathbb{N}:n\leq x\}.$ In particular, if $\varepsilon>0$ and $M:=M(m)\leq m^{1-\varepsilon},$ then the Bohnenblust-Hille inequality restricted to sums over $M$ indexes is contractive. Comment: This preprint was incorporated in the Arxiv preprint number arXiv:1409.6769 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1705.06307 |
| رقم الأكسشن: | edsarx.1705.06307 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |