Boundedness of the Equiconvergent Operators on the Sphere

Abstract:

      Let Rⁿ be an n-dimensional Euclidean space with n≥ 3. Denote by Ω_n the unit sphere in Rⁿ. For a function f∈L(Ω_n) we denote by E_N^δ(f) the equiconvergent operator of Cesaro means of order δ of the Fourier-Laplace series of f. The special value λ:= (n-2)/2 of δ is known as the critical index. For 0 < δ≤λ, we set p₀:= (2λ)/(λ+δ). The main aim of this paper is to prove that (?) with l > 1.