Optimal Hardy–Littlewood type inequalities for m-linear forms on $${\ell_{p}}$$ℓp spaces with $${1\leq p\leq m}$$1≤p≤m

@article{Arajo2015OptimalHT,
  title={Optimal Hardy–Littlewood type inequalities for m-linear forms on \$\$\{\ell_\{p\}\}\$\$ℓp spaces with \$\$\{1\leq p\leq m\}\$\$1≤p≤m},
  author={Gustavo Ara{\'u}jo and Daniel Pellegrino},
  journal={Archiv der Mathematik},
  year={2015},
  volume={105},
  pages={285-295}
}
AbstractThe Hardy–Littlewood inequalities for m-linear forms on $${\ell _{p}}$$ℓp spaces are stated for $${p > m}$$p>m. In this paper, among other results, we investigate similar results for $${1\leq p\leq m.}$$1≤p≤m. Let $${\mathbb{K}}$$K be $${ \mathbb{R}}$$R or $${\mathbb{C}}$$C and $${m\geq 2}$$m≥2 be a positive integer. Our main results are the following sharp inequalities: (i)If $${\left( r,p\right) \in \left( \lbrack 1,2]\times \lbrack 2,2m)\right) \cup \left( \lbrack 1,\infty )\times… CONTINUE READING

References

Publications referenced by this paper.
SHOWING 1-10 OF 25 REFERENCES

D

N. Albuquerque, F. Bayart
  • Pellegrino, J.B. Seoane–Sepúlveda, Sharp generalizations of the multilinear Bohnenblust–Hille inequality, J. Funct. Anal. 266
  • 2014
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

Majorant series

H. P. Boas
  • J. Korean Math. Soc. 37
  • 2000
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Lower Bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars

D. Diniz, G. A. Muñoz-Fernádez, D. Pellegrino, J. B. Seoane-Sepúlveda
  • Proc. Amer. Math. Soc. 142
  • 2014

The Bohr radius of the n–dimensional polydisc is equivalent to √ (logn)/n

F. Bayart, D. Pellegrino, J. B. Seoane-Sepúlveda
  • Adv. Math. 264
  • 2014
VIEW 1 EXCERPT

Seoane-Seplveda, On the optimality of teh complex Bohnenblust–HIlle inequality, arXiv 1301.1539v3 [mathFA

J. R. Campos, G. A. Munoz-Fernndez, J.B.D. Pellegrino
  • 2013
VIEW 1 EXCERPT