Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The $ H\sp p$-boundedness of the Riesz means for the eigenfunction expansions for elliptic operators with constant coefficients


Authors: He Ping Liu and Shan Zhen Lu
Journal: Proc. Amer. Math. Soc. 122 (1994), 487-494
MSC: Primary 35P05; Secondary 35J30, 42B30
DOI: https://doi.org/10.1090/S0002-9939-1994-1198458-3
MathSciNet review: 1198458
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study the bounded property of the Riesz means for the eigenfunction expansions for elliptic operators on the Hardy spaces. Our result generalizes the classical result due to Sjölin and Stein-Taibleson-Weiss on the Bochner-Riesz means.


References [Enhancements On Off] (What's this?)

  • [1] C. Fefferman and E. M. Stein, $ {H^p}$ spaces of several variables, Acta Math. 129 (1972), 137-193. MR 0447953 (56:6263)
  • [2] R. H. Latter, A characterization of $ {H^p}({\mathbb{R}^n})$ in terms of atoms, Studia Math. 62 (1978), 93-101. MR 0482111 (58:2198)
  • [3] Z. X. Liu and S. Z. Lu, Applications of Hörmander multiplier theorem to approximation in real Hardy spaces, Lecture Notes in Math., vol. 1494, Springer, Berlin and New York, 1991, pp. 119-129. MR 1187072 (94a:46028)
  • [4] J. Peetre, Remark on eigenfunction expansions for elliptic operators with constant coefficients, Math. Scand. 15 (1964), 83-92. MR 0178252 (31:2510)
  • [5] P. Sjölin, Convolution with oscillating kernels in $ {H^p}$ spaces, J. London Math. Soc. 23 (1981), 442-454. MR 616550 (82h:42024)
  • [6] E. M. Stein, Localization and summability of multiple Fourier series, Acta Math. 100 (1958), 93-147. MR 0105592 (21:4331)
  • [7] E. M. Stein, M. H. Taibleson, and G Weiss, Weak type estimates for maximal operators on certain $ {H^p}$ spaces, Rend. Circ. Mat. Palermo Suppl. 1 (1981), 81-97. MR 639468 (83c:42017)
  • [8] M. H. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Asterisque 77 (1980), 68-149. MR 604370 (83g:42012)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35P05, 35J30, 42B30

Retrieve articles in all journals with MSC: 35P05, 35J30, 42B30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1198458-3
Keywords: Riesz means, Hardy space
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society