Vol. 9, No. 5, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Bohnenblust–Hille inequalities for Lorentz spaces via interpolation

Andreas Defant and Mieczysław Mastyło

Vol. 9 (2016), No. 5, 1235–1258

We prove that the Lorentz sequence space 2m(m+1),1 is, in a precise sense, optimal among all symmetric Banach sequence spaces satisfying a Bohnenblust–Hille-type inequality for m-linear forms or m-homogeneous polynomials on n . Motivated by this result we develop methods for dealing with subtle Bohnenblust–Hille-type inequalities in the setting of Lorentz spaces. Based on an interpolation approach and the Blei–Fournier inequalities involving mixed-type spaces, we prove multilinear and polynomial Bohnenblust–Hille-type inequalities in Lorentz spaces with subpolynomial and subexponential constants. An application to the theory of Dirichlet series improves a deep result of Balasubramanian, Calado and Queffélec.

Bohnenblust–Hille inequality, Dirichlet polynomials, Dirichlet series, homogeneous polynomials, interpolation spaces, Lorentz spaces
Mathematical Subject Classification 2010
Primary: 46B70, 47A53
Received: 14 January 2016
Revised: 12 February 2016
Accepted: 30 March 2016
Published: 29 July 2016
Andreas Defant
Institut für Mathematik
Carl von Ossietzky Universität
Postfach 2503
D-26111 Oldenburg
Mieczysław Mastyło
Faculty of Mathematics and Computer Science
Adam Mickiewicz University in Poznań
Umultowska 87
61-614 Poznań