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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 926527, 15 pages
http://dx.doi.org/10.1155/2011/926527
Research Article

𝑝 -Carleson Measures for a Class of Hardy-Orlicz Spaces

School of Mathematics, Trinity College Dublin, Dublin 2, Ireland

Received 10 December 2010; Accepted 19 April 2011

Academic Editor: Hans Engler

Copyright © 2011 Benoît Florent Sehba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Carleson, “Interpolations by bounded analytic functions and the corona problem,” Annals of Mathematics, vol. 76, pp. 547–559, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. P. L. Duren, “Extension of a theorem of Carleson,” Bulletin of the American Mathematical Society, vol. 75, pp. 143–146, 1969. View at Publisher · View at Google Scholar
  3. I. V. Videnskiĭ, “An analogue of Carleson measures,” Doklady Akademii Nauk SSSR, vol. 298, no. 5, pp. 1042–1047, 1988. View at Google Scholar
  4. L. Hörmander, “Lp estimates for (pluri-) subharmonic functions,” Mathematica Scandinavica, vol. 20, pp. 65–78, 1967. View at Google Scholar · View at Zentralblatt MATH
  5. D. H. Luecking, “Embedding derivatives of Hardy spaces into Lebesgue spaces,” Proceedings of the London Mathematical Society, vol. 63, no. 3, pp. 595–619, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. C. Power, “Hörmander's Carleson theorem for the ball,” Glasgow Mathematical Journal, vol. 26, no. 1, pp. 13–17, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. P. Lefèvre, D. Li, H. Queffélec, and L. Rodríguez-Piazza, Composition Operators on Hardy-Orlicz Spaces, vol. 207 of Memoirs of the American Mathematical Society, 2010.
  8. S. Charpentier, “Composition operators on Hardy-Orlicz spaces on the ball,” to appear in Integral Equations and Operator Theory.
  9. A. Bonami and S. Grellier, “Hankel operators and weak factorization for Hardy-Orlicz spaces,” Colloquium Mathematicum, vol. 118, no. 1, pp. 107–132, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. A. Bonami and B. Sehba, “Hankel operators between Hardy-Orlicz spaces and products of holomorphic functions,” Revista de la Unión Matemática Argentina, vol. 50, no. 2, pp. 187–199, 2009. View at Google Scholar
  11. B. F. Sehba, “On some equivalent definitions of ρ-Carleson measures on the unit ball,” Acta Universitatis Szegediensis, vol. 75, no. 3-4, pp. 499–525, 2009. View at Google Scholar
  12. R. Zhao, “On logarithmic Carleson measures,” Acta Universitatis Szegediensis, vol. 69, no. 3-4, pp. 605–618, 2003. View at Google Scholar · View at Zentralblatt MATH
  13. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer, New York, NY, USA, 2004.
  14. S.-I. Ueki and L. Luo, “Compact weighted composition operators and multiplication operators between Hardy spaces,” Abstract and Applied Analysis, vol. 2008, Article ID 196498, 12 pages, 2008. View at Google Scholar · View at Zentralblatt MATH
  15. R. Zhao and K. Zhu, “Theory of Bergman spaces in the unit ball of n,” Mémoires de la Société Mathématique de France. Nouvelle Série, no. 115, 2008. View at Google Scholar · View at Zentralblatt MATH
  16. A. Aleman and A. G. Siskakis, “An integral operator on Hp,” Complex Variables, vol. 28, no. 2, pp. 149–158, 1995. View at Google Scholar · View at Zentralblatt MATH
  17. A. Aleman and A. G. Siskakis, “Integration operators on Bergman spaces,” Indiana University Mathematics Journal, vol. 46, no. 2, pp. 337–356, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. K. R. M. Attele, “Analytic multipliers of Bergman spaces,” The Michigan Mathematical Journal, vol. 31, no. 3, pp. 307–319, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. S. Axler, “Multiplication operators on Bergman spaces,” Journal für die Reine und Angewandte Mathematik, vol. 336, pp. 26–44, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. S. Axler, “Zero multipliers of Bergman spaces,” Canadian Mathematical Bulletin, vol. 28, no. 2, pp. 237–242, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. Z. Cucković and R. Zhao, “Weighted composition operators between different weighted Bergman spaces and different Hardy spaces,” Illinois Journal of Mathematics, vol. 51, no. 2, pp. 479–498, 2007. View at Google Scholar
  22. N. S. Feldman, “Pointwise multipliers from the Hardy space to the Bergman space,” Illinois Journal of Mathematics, vol. 43, no. 2, pp. 211–221, 1999. View at Google Scholar · View at Zentralblatt MATH
  23. S. Janson, “On functions with conditions on the mean oscillation,” Arkiv för Matematik, vol. 14, no. 2, pp. 189–196, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. D. H. Luecking, “Multipliers of Bergman spaces into Lebesgue spaces,” Proceedings of the Edinburgh Mathematical Society. Series II, vol. 29, no. 1, pp. 125–131, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. F. Pérez-González, J. Rättyä, and D. Vukotić, “On composition operators acting between Hardy and weighted Bergman spaces,” Expositiones Mathematicae, vol. 25, no. 4, pp. 309–323, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. A. G. Siskakis and R. Zhao, “A Volterra type operator on spaces of analytic functions,” in Function Spaces, vol. 232 of Contemporary Mathematics, pp. 299–311, American Mathematical Society, Providence, RI, USA, 1999. View at Google Scholar · View at Zentralblatt MATH
  27. W. Smith, “Composition operators between Bergman and Hardy spaces,” Transactions of the American Mathematical Society, vol. 348, no. 6, pp. 2331–2348, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. S. Stević, “On an integral operator on the unit ball in n,” Journal of Inequalities and Applications, no. 1, pp. 81–88, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. S. Stević, “On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball,” Journal of Mathematical Analysis and Applications, vol. 354, no. 2, pp. 426–434, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. R. Zhao, “Pointwise multipliers from weighted Bergman spaces and Hardy spaces to weighted Bergman spaces,” Annales Academiæ Scientiarium Fennicæ. Mathematica, vol. 29, no. 1, pp. 139–150, 2004. View at Google Scholar · View at Zentralblatt MATH
  31. W. S. Smith, “BMOρ and Carleson measures,” Transactions of the American Mathematical Society, vol. 287, no. 1, pp. 107–126, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet