Divergent Laguerre series
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- by Krzysztof Stempak PDF
- Proc. Amer. Math. Soc. 129 (2001), 1123-1126 Request permission
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
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Additional Information
- Krzysztof Stempak
- Affiliation: Instytut Matematyczny Politechniki Wrocławskiej, Wyb. Wyspianskiego 27, 50-370 Wrocław, Poland
- Email: stempak@im.pwr.wroc.pl
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1709766