BMO- and VMO-spaces of slice hyperholomorphic functions

Gantner, Jonathan; González-Cervantes, J. Oscar; Janssens, Tim

doi:10.48550/arxiv.1609.01633

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Carleson Measures In Bergman Spaces1

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2017

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“…Let U ⊆ H be an axially symmetric s-domain. For p > 0, we define the slice regular Bergman space A p (U ) as the quaternionic right linear space of all slice regular functions on U such that (16) sup…”

Section: Carleson Measures In Bergman Spacesmentioning

confidence: 99%

Carleson measures for Hardy and Bergman spaces in the quaternionic unit ball

Sabadini

Saracco

2017

J. London Math. Soc.

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We study a characterization of slice Carleson measures and of Carleson measures for both the Hardy spaces Hp(B) and the Bergman spaces Ap(B) of the quaternionic unit ball B. In the case of Bergman spaces, the characterization is done in terms of the axially symmetric completion of a pseudohyperbolic disc in a complex plane. We also show that a characterization in terms of pseudo-hyperbolic balls is not possible

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Section: Carleson Measures In Bergman Spacesmentioning

confidence: 99%