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Remarks on the Bohnenblust-Hille inequalities. (English) Zbl 07272893
Summary: We revisit the Bohnenblust-Hille multilinear and polynomial inequalities and prove some new properties. Our main result is a multilinear version of a recent result on polynomials whose monomials have a uniformly bounded number of variables.
MSC:
47A63 Linear operator inequalities
47H60 Multilinear and polynomial operators
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[1] N. Albuquerque, G. Arau´jo, W. Cavalcante, T. Nogueira, D. Nu´n˜ez-Alarco´n, D. Pellegrino, P. Rueda, On summability of multilinear operators and applications.Ann. Funct. Anal.9(2018), no. 4, 574-590. · Zbl 1442.47007
[2] N. Albuquerque, F. Bayart, D. Pellegrino, J. B. Seoane-Sepu´lveda, Sharp generalizations of the multilinear Bohnenblust-Hille inequality.J. Funct. Anal.266(2014), 3726-3740. · Zbl 1319.46035
[3] G. Arau´jo, D. Pellegrino, A Gale-Berlekamp permutation-switching problem in higher dimensions.European J. Combin.77(2019), 17-30.
[4] S. Arunachalam, S. Chakraborty, M. Koucky, N. Saurabh, R. de Wolf, Improved bounds on Fourier entropy and Min-entropy.Electron. Colloquium Comput. Complexity(ECCC)25(2018), 167.
[5] F. Bayart, D. Pellegrino, J. B. Seoane-Sepu´lveda, The Bohr radius of thepffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n-dimensional polydisc is equivalent toðlognÞ=n:Adv. Math.264(2014), 726-746. · Zbl 1331.46037
[6] H. P. Boas, Majorant series.J. Korean Math. Soc.37(2000), 321-337. · Zbl 0965.32001
[7] H. F. Bohnenblust, E. Hille, On the absolute convergence of Dirichlet series.Ann. of Math.32(1931), 600-622. · JFM 57.0266.05
[8] D. Carando, A. Defant, P. Sevilla-Peris, The Bohnenblust-Hille inequality combined with an inequality of Helson.Proc. Amer. Math. Soc.143(2015), no. 12, 5233-5238. · Zbl 1329.32001
[9] W. Cavalcante, D. Pellegrino, Bohnenblust-Hille inequalities: analytical and computational aspects.An. Acad. Brasil. Cieˆnc.91(2019), no. 1, suppl. 1, e20170398 (19 pages). · Zbl 07212611
[10] J. E. Littlewood, On bounded bilinear forms in an infinite number of variables.Quart. J.(Oxford Ser.)1(1930), 164-174. · JFM 56.0335.01
[11] M. Maia, T. Nogueira, D. Pellegrino, The Bohnenblust-Hille inequality for polynomials whose monomials have a uniformly bounded number of variables.Integr. Equ. Oper. Theory88(2017), 143-149. · Zbl 1378.32001
[12] A. Montanaro, Some applications of hypercontractive inequalities in quantum information theory.J. Math. Phys.53(2012), no. 12, 122206 (15 pages). · Zbl 1278.81045
[13] D. Nu´n˜ez-Alarco´n, A note on the polynomial Bohnenblust-Hille inequality.J. Math. Anal. Appl.407(2013), no. 1, 179-181.
[14] D. Pellegrino, E. Teixeira, Towards sharp Bohnenblust-Hille constantes.Commun. Contemp. Math.20(2018), no. 3, 1750029 (33 pages). · Zbl 1403.46037
[15] D. Tomaz, Hardy-Littlewood inequalities for multipolynomials.Adv. Oper. Theory4 (2019), no. 3, 688-697. · Zbl 1423.47057
[16] F.
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