On convergence of orthogonal series of Bessel functions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Volume 27 (1973) no. 3, p. 507-525 
@article{ASNSP_1973_3_27_3_507_0,
     author = {Benedek, A. and Panzone, R.},
     title = {On convergence of orthogonal series of Bessel functions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 27},
     number = {3},
     year = {1973},
     pages = {507-525},
     zbl = {0273.42013},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1973_3_27_3_507_0}
}

Benedek, A.; Panzone, R. On convergence of orthogonal series of Bessel functions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Volume 27 (1973) no. 3, pp. 507-525. http://www.numdam.org/item/ASNSP_1973_3_27_3_507_0/

[1] Benedek A. and Panzone R., On mean convergence of Fourier-Bessel series of negative order, Studies in App. Math. Vol. 4 n° 3, (1971), 281-292. | MR 310535 | Zbl 0218.42012

[2] Benedek A. and Panzone R., Mean convergence of Bessel and Dini series, Notices AMS, 18, n0 6, (1971), p. 951 (to appear Rev. UMA, vol. 26, (1972))-

[3] Muckenhoupt B., Mean convergence of Hermite and Laguerre series, II, TAMS, 147, (1970), 433-460. | MR 256051 | Zbl 0191.07602

[4] Titchmarsh, E.C., Eigenfunction expansions I, Oxford, (1962).

[5] Watson, G.N., A treatise on the theory of Bessel functions, Cambridge, (1952). | Zbl 0174.36202

[6] Wing, G.M., The mean convergence of orthogonal series, Amer. J. of Math., LXXII, (1950), 792-808. | MR 37923 | Zbl 0041.38515