Compact embedding derivatives of Hardy spaces into Lebesgue spaces
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Abstract:
We characterize the positive Borel measures such that the differentiation operator of order $n\in \mathbb {N}\cup \{0\}$ is compact from the Hardy space $H^p$ into $L^q(\mu )$, $0<p,q<\infty$.References
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Additional Information
- José Ángel Peláez
- Affiliation: Departamento de Análisis Matemático, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain
- Email: japelaez@uma.es
- Received by editor(s): December 8, 2014
- Received by editor(s) in revised form: February 12, 2015
- Published electronically: June 30, 2015
- Additional Notes: The author was supported in part by the Ramón y Cajal program of MICINN (Spain), Ministerio de Educación y Ciencia, Spain, (MTM2011-25502 and MTM2014-52865-P), from La Junta de Andalucía, (FQM210) and (P09-FQM-4468).
- Communicated by: Pamela B. Gorkin
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1095-1107
- MSC (2010): Primary 30H10
- DOI: https://doi.org/10.1090/proc12763
- MathSciNet review: 3447663