Book contents
- Frontmatter
- Contents
- Introduction
- Part 1 Bohr’s Problem and Complex Analysis on Polydiscs
- Part 2 Advanced Toolbox
- Part 3 Replacing Polydiscs by Other Balls
- 18 Hardy–Littlewood Inequality
- 19 Bohr Radii in ℓp Spaces and Unconditionality
- 20 Monomial Convergence in Banach Sequence Spaces
- 21 Dineen’s Problem
- 22 Back to Bohr Radii
- Part 4 Vector-Valued Aspects
- References
- Symbol Index
- Subject Index
22 - Back to Bohr Radii
from Part 3 - Replacing Polydiscs by Other Balls
Published online by Cambridge University Press: 19 July 2019
Book contents
- Frontmatter
- Contents
- Introduction
- Part 1 Bohr’s Problem and Complex Analysis on Polydiscs
- Part 2 Advanced Toolbox
- Part 3 Replacing Polydiscs by Other Balls
- 18 Hardy–Littlewood Inequality
- 19 Bohr Radii in ℓp Spaces and Unconditionality
- 20 Monomial Convergence in Banach Sequence Spaces
- 21 Dineen’s Problem
- 22 Back to Bohr Radii
- Part 4 Vector-Valued Aspects
- References
- Symbol Index
- Subject Index
Summary
The Bohr radius for p-norms was introduced and studied in Chapter 19. There it was shown that unconditional basis constants of the monomials in spaces of m-homogeneous polynomials and Bohr radii are, in a certain sense, reciprocal to each other. In Chapter 21 the Gordon-Lewis cycle of ideas was developed to study these unconditional basis constants. Relating unconditional basis constants, Gordon-Lewis constants and projection constants of spaces of m-homogeneous polynomials gives a new proof of the lower bound for the Bohr radius for p-norms.
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- Information
- Dirichlet Series and Holomorphic Functions in High Dimensions , pp. 555 - 564Publisher: Cambridge University PressPrint publication year: 2019