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ON SOME NEW THEOREMS ON MULTIPLIERS IN HARMONIC FUNCTION SPACES IN HIGHER DIMENSION II

  • Arsenovic, Milos ;
  • Shamoyan, Romi F.
  • Received : 2011.08.13
  • Published : 2013.09.30

Abstract

We present various new sharp assertions on multipliers in mixed norm, weighted Hardy and new Lizorkin-Triebel spaces of harmonic functions in higher dimension. Some results are new even in onedimensional case.

Keywords

multipliers;spaces of harmonic functions;Bergman type mixed norm spaces;spherical harmonics

References

  1. A. B. Alexandrov, Essays on non Locally Convex Hardy Classes, in Complex Analysis and Spectral Theory, 1-89, Lecture Notes in Mathematics 864, 1981.
  2. A. B. Alexandrov, On decrease in mean at the boundary of harmonic functions, in Russian, Algebra i Analiz, Tom 7 (1995), no. 4, 1-49.
  3. M. Arsenovic and R. F. Shamoyan, Sharp theorems on multipliers and distances in harmonic function spaces in higher dimension, J. Siberian Federal University. Mathematics & Physics 5 (2012), no. 3, 291-302.
  4. M. Djrbashian and F. Shamoian, Topics in the theory of $A_{\alpha}^{p}$ classes, Teubner Texts in Mathematics, 105. BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1988.
  5. M. Jevtic and M. Pavlovic, Harmonic Bergman functions on the unit ball in $\mathbb{R}^n$, Acta Math. Hungar. 85 (1999), no. 1-2, 81-96. https://doi.org/10.1023/A:1006620929091
  6. M. Jevtic and M. Pavlovic, Harmonic Besov spaces on the unit ball in $\mathbb{R}^n$, Rocky Mountain J. Math. 31 (2001), no. 4, 1305-1316. https://doi.org/10.1216/rmjm/1021249442
  7. J. M. Ortega and J. Fabrega, Holomorphic Triebel-Lizorkin Spaces, J. Funct. Anal. 151 (1997), no. 1, 177-212. https://doi.org/10.1006/jfan.1997.3138
  8. M. Pavlovic, Convolution in the harmonic Hardy space hp with 0 < p < 1, Proc. Amer. Math. Soc. 109 (1990), no. 1, 129-134.
  9. M. Pavlovic, Multipliers of the vanishing Hardy classes, Publ. Inst. Math. (Beograd) (N.S.) 52(66) (1992), 34-36.
  10. R. F. Shamoyan, On multipliers from Bergman type to Hardy spaces in polydisk, Ukrain. Mat. Zh. 52 (2000), no. 10, 1405-1414; translation in Ukrainian Math. J. 52 (2000), no. 10, 1606-1617.
  11. R. F. Shamoyan, Holomorphic Lizorkin Triebel type spaces in the unit polydisk, Izv. NAN Ar-menii 3 (2002), 57-78.
  12. R. F. Shamoyan and A. Abkar, On multipliers of spaces of harmonic functions in the unit ball of $\mathbb{R}^n$, J. Inequalities and Special Functions 3 (2012), no. 1, 1-9.
  13. A. Shields and D. Williams, Bounded projections, duality and multipliers in spaces of harmonic functions, J. Reine Angew. Math. 299/300 (1978), 256-279.
  14. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971.
  15. M. Zakaryan, Integral representations and duality in weighted spaces of harmonic functions in the unit ball, in Russian, Ph.D. Thesis, Erevan State University, 1999.

Cited by

  1. A characterization of the inclusions between mixed norm spaces vol.429, pp.2, 2015, https://doi.org/10.1016/j.jmaa.2015.04.061
  2. Corrigendum to “A characterization of the inclusions between mixed norm spaces” [J. Math. Anal. Appl. 429 (2) (2015) 942–955] vol.433, pp.2, 2016, https://doi.org/10.1016/j.jmaa.2015.08.053