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)

 
 

 

Divergent Laguerre series


Author: Krzysztof Stempak
Journal: Proc. Amer. Math. Soc. 129 (2001), 1123-1126
MSC (1991): Primary 42C10; Secondary 42C99
DOI: https://doi.org/10.1090/S0002-9939-00-05657-4
Published electronically: October 16, 2000
MathSciNet review: 1709766
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove failure of a.e. convergence of partial sums of Laguerre expansions of $L^{p}$ functions for $p>4$. The idea which is used goes back to Stanton and Tomas. We follow Meaney's paper (1983), where divergence results were proved in the Jacobi polynomial case.


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

  • [Ma] Markett, C., Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37. MR 83j:40004
  • [Me] Meaney, C., Divergent Jacobi polynomial series, Proc. Amer. Math. Soc. 87 (1983), 459-462. MR 84c:42040
  • [M] Muckenhoupt, B., Equiconvergence and almost everywhere convergence of Hermite and Laguerre series, SIAM J. Math. Anal. 1 (1970), 295-321. MR 42:4948
  • [Po] Pollard, H., The mean convergence of orthogonal series II, Trans. Amer. Math. Soc. 63 (1948), 355-367. MR 9:426e
  • [St] Stempak, K., Transplanting maximal inequalities between Laguerre and Hankel multipliers, Monats. Math. 122 (1996), 187-197. MR 97g:42010
  • [Sz] Szegö, G., Orthogonal Polynomials, Colloquium Publications, vol.23, American Mathematical Society, New York, 1939. MR 1:14b

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42C10, 42C99

Retrieve articles in all journals with MSC (1991): 42C10, 42C99


Additional Information

Krzysztof Stempak
Affiliation: Instytut Matematyczny Politechniki Wrocławskiej, Wyb. Wyspianskiego 27, 50-370 Wrocław, Poland
Email: stempak@im.pwr.wroc.pl

DOI: https://doi.org/10.1090/S0002-9939-00-05657-4
Keywords: Laguerre polynomials and functions, divergence almost everywhere
Received by editor(s): March 19, 1999
Received by editor(s) in revised form: July 2, 1999
Published electronically: October 16, 2000
Additional Notes: This research was supported in part by KBN grant # 2 PO3A 048 and European Commission via the TMR network “Harmonic Analysis”, contract no. ERB FMRX-CT970159.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society