## Banach Journal of Mathematical Analysis

### Solid cores and solid hulls of weighted Bergman spaces

#### Abstract

We determine the solid hull for $2\lt p\lt \infty$ and the solid core for $1\lt p\lt 2$ of weighted Bergman spaces $A_{\mu}^{p},1\lt p\lt \infty$, of analytic functions on the disk and on the whole complex plane, for a very general class of nonatomic positive bounded Borel measures $\mu$. New examples are presented. Moreover, we show that the space $A_{\mu}^{p},1\lt p\lt \infty$, is solid if and only if the monomials are an unconditional basis of this space.

#### Article information

Source
Banach J. Math. Anal., Volume 13, Number 2 (2019), 468-485.

Dates
Accepted: 10 December 2018
First available in Project Euclid: 26 February 2019

https://projecteuclid.org/euclid.bjma/1551150773

Digital Object Identifier
doi:10.1215/17358787-2018-0049

Mathematical Reviews number (MathSciNet)
MR3927883

Zentralblatt MATH identifier
07045468

#### Citation

Bonet, José; Lusky, Wolfgang; Taskinen, Jari. Solid cores and solid hulls of weighted Bergman spaces. Banach J. Math. Anal. 13 (2019), no. 2, 468--485. doi:10.1215/17358787-2018-0049. https://projecteuclid.org/euclid.bjma/1551150773

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