Banach Journal of Mathematical Analysis

Solid cores and solid hulls of weighted Bergman spaces

José Bonet, Wolfgang Lusky, and Jari Taskinen

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Abstract

We determine the solid hull for 2<p< and the solid core for 1<p<2 of weighted Bergman spaces Aμp,1<p<, of analytic functions on the disk and on the whole complex plane, for a very general class of nonatomic positive bounded Borel measures μ. New examples are presented. Moreover, we show that the space Aμp,1<p<, 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
Received: 9 July 2018
Accepted: 10 December 2018
First available in Project Euclid: 26 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1551150773

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

Mathematical Reviews number (MathSciNet)
MR3927883

Zentralblatt MATH identifier
07045468

Subjects
Primary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Secondary: 46B15: Summability and bases [See also 46A35]

Keywords
weighted Bergman spaces solid hulls solid cores

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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References

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