Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points

Let ∑be the unit sphere in the n-dimensional Euclidean space R~n.For a functionf ∈L(∑) denote by σ~δ(f) the Cesàro means of order δ of the Fourier-Laplace series of f.Thespecial value λ∶=(n-2)/2 of δ is known as the critical index.In the case when n is even,this paper provesthe existence of the‘rare’sequence {n} such that the summability1/N sum from k=1 to N σ~λ(f)(x)→f(x),N→∞takes place at each Lebesgue point satisfying some antipole conditions.