Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Mixed Bohr radius in several variables
HTML articles powered by AMS MathViewer

by Daniel Galicer, Martín Mansilla and Santiago Muro PDF
Trans. Amer. Math. Soc. 373 (2020), 777-796 Request permission

Abstract:

Let $K(B_{\ell _p^n},B_{\ell _q^n})$ be the $n$-dimensional $(p,q)$-Bohr radius for holomorphic functions on $\mathbb {C}^n$. That is, $K(B_{\ell _p^n},B_{\ell _q^n})$ denotes the greatest number $r\geq 0$ such that for every entire function $f(z)=\sum _{\alpha } a_{\alpha } z^{\alpha }$ in $n$-complex variables, we have the following (mixed) Bohr-type inequality: \begin{equation*} \sup _{z \in r \cdot B_{\ell _q^n}} \sum _{\alpha } \vert a_{\alpha } z^{\alpha } \vert \leq \sup _{z \in B_{\ell _p^n}} \vert f(z) \vert , \end{equation*} where $B_{\ell _r^n}$ denotes the closed unit ball of the $n$-dimensional sequence space $\ell _r^n$.

For every $1 \leq p, q \leq \infty$, we exhibit the exact asymptotic growth of the $(p,q)$-Bohr radius as $n$ (the number of variables) goes to infinity.

References
Similar Articles
Additional Information
  • Daniel Galicer
  • Affiliation: Departamento de Matemática - Pab I, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina; and IMAS-CONICET
  • MR Author ID: 915441
  • Email: dgalicer@dm.uba.ar
  • Martín Mansilla
  • Affiliation: Departamento de Matemática - Pab I, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina; and IMAS-CONICET
  • Email: mmansilla@dm.uba.ar
  • Santiago Muro
  • Affiliation: Departamento de Matemática - Pab I, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina; and CIFASIS-CONICET, Rosario, Argentina
  • MR Author ID: 822942
  • Email: muro@cifasis-conicet.gov.ar
  • Received by editor(s): December 21, 2017
  • Received by editor(s) in revised form: May 30, 2018
  • Published electronically: November 5, 2019
  • Additional Notes: This work was partially supported by projects CONICET PIP 11220130100329CO, ANPCyT PICT 2015-2224, ANPCyT PICT 2015-2299, ANPCyT PICT 2015-3085, UBACyT 20020130100474BA, UBACyT 20020130300052BA, UBACyT 20020130300057BA
    The second author was supported by a CONICET doctoral fellowship
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 777-796
  • MSC (2010): Primary 32A05, 32A22; Secondary 46B15, 46B20, 46G25, 46E50
  • DOI: https://doi.org/10.1090/tran/7870
  • MathSciNet review: 4068249