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Compact embedding derivatives of Hardy spaces into Lebesgue spaces


Author: José Ángel Peláez
Journal: Proc. Amer. Math. Soc. 144 (2016), 1095-1107
MSC (2010): Primary 30H10
DOI: https://doi.org/10.1090/proc12763
Published electronically: June 30, 2015
MathSciNet review: 3447663
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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 $.


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  • [1] Patrick Ahern and Joaquim Bruna, Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball of $ {\bf C}^n$, Rev. Mat. Iberoamericana 4 (1988), no. 1, 123-153. MR 1009122 (90h:32011), https://doi.org/10.4171/RMI/66
  • [2] A. Benedek and R. Panzone, The space $ L^{p}$, with mixed norm, Duke Math. J. 28 (1961), 301-324. MR 0126155 (23 #A3451)
  • [3] Oscar Blasco de la Cruz and Hans Jarchow, A note on Carleson measures for Hardy spaces, Acta Sci. Math. (Szeged) 71 (2005), no. 1-2, 371-389. MR 2160373 (2006d:30048)
  • [4] W. S. Cohn and I. E. Verbitsky, Factorization of tent spaces and Hankel operators, J. Funct. Anal. 175 (2000), no. 2, 308-329. MR 1780479 (2001g:42047), https://doi.org/10.1006/jfan.2000.3589
  • [5] William Cohn, Sarah H. Ferguson, and Richard Rochberg, Boundedness of higher order Hankel forms, factorization in potential spaces and derivations, Proc. London Math. Soc. (3) 82 (2001), no. 1, 110-130. MR 1794259 (2001k:47036), https://doi.org/10.1112/S0024611500012727
  • [6] R. R. Coifman, Y. Meyer, and E. M. Stein, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. 62 (1985), no. 2, 304-335. MR 791851 (86i:46029), https://doi.org/10.1016/0022-1236(85)90007-2
  • [7] Peter L. Duren, Theory of $ H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655 (42 #3552)
  • [8] C. Fefferman and E. M. Stein, $ H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137-193. MR 0447953 (56 #6263)
  • [9] Daniel H. Luecking, Forward and reverse Carleson inequalities for functions in Bergman spaces and their derivatives, Amer. J. Math. 107 (1985), no. 1, 85-111. MR 778090 (86g:30002), https://doi.org/10.2307/2374458
  • [10] Daniel H. Luecking, Embedding derivatives of Hardy spaces into Lebesgue spaces, Proc. London Math. Soc. (3) 63 (1991), no. 3, 595-619. MR 1127151 (92k:42030), https://doi.org/10.1112/plms/s3-63.3.595
  • [11] Daniel H. Luecking, Embedding theorems for spaces of analytic functions via Khinchine's inequality, Michigan Math. J. 40 (1993), no. 2, 333-358. MR 1226835 (94e:46046), https://doi.org/10.1307/mmj/1029004756
  • [12] Miroslav Pavlović, On the Littlewood-Paley $ g$-function and Calderón's area theorem, Expo. Math. 31 (2013), no. 2, 169-195. MR 3057123, https://doi.org/10.1016/j.exmath.2013.01.006
  • [13] José Ángel Peláez and Jouni Rättyä, Embedding theorems for Bergman spaces via harmonic analysis, Math. Ann. 362 (2015), no. 1-2, 205-239. MR 3343875, https://doi.org/10.1007/s00208-014-1108-5
  • [14] K. Zhu and R. Zhao, Theory of Bergman spaces in the unit ball, Memoires de la SFM 115 (2008).

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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

DOI: https://doi.org/10.1090/proc12763
Keywords: Hardy spaces, tent spaces, Carleson measures, differentiation operator, compact operators.
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
Article copyright: © Copyright 2015 American Mathematical Society

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