Kushpel, A. K.2021-02-172025-09-182021-02-172025-09-182020Kushpel, A. K. (2020). "On the Lebesgue Constants", Ukrainian Mathematical Journal, Vol. 71, No. 8, pp. 1224-1233.0041-59951573-9376https://doi.org/10.1007/s11253-019-01709-5https://hdl.handle.net/20.500.12416/10527We present the solution of a classical problem of approximation theory about the sharp asymptotics of Lebesgue constants or the norms of Fourier-Laplace projections on the real sphere S-d, in complex P-d (C) and quaternionic P-d(H) projective spaces, and in the Cayley elliptic plane P-16(Cay). In particular, these results supplement the sharp asymptotics established by Fejer (1910) in the case of S-1 and by Gronwall (1914) in the case of S-2.eninfo:eu-repo/semantics/closedAccessArticle10.1007/s11253-019-01709-52-s2.0-85077142619