Divergent Laguerre series

Stempak, Krzysztof

doi:10.1090/S0002-9939-00-05657-4

Divergent Laguerre series
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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

C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), no. 1, 19–37 (English, with Russian summary). MR 662701, DOI 10.1007/BF02073769
Christopher Meaney, Divergent Jacobi polynomial series, Proc. Amer. Math. Soc. 87 (1983), no. 3, 459–462. MR 684639, DOI 10.1090/S0002-9939-1983-0684639-4
Benjamin Muckenhoupt, Equiconvergence and almost everywhere convergence of Hermite and Laguerre series, SIAM J. Math. Anal. 1 (1970), 295–321. MR 270055, DOI 10.1137/0501027
Garrett Birkhoff and Morgan Ward, A characterization of Boolean algebras, Ann. of Math. (2) 40 (1939), 609–610. MR 9, DOI 10.2307/1968945
Krzysztof Stempak, Transplanting maximal inequalities between Laguerre and Hankel multipliers, Monatsh. Math. 122 (1996), no. 2, 187–197. MR 1402638, DOI 10.1007/BF01297769
T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058