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

Let n1 be the unit sphere in the n-dimensional Euclidean space n. For a funcion L( n1 ) denote by N(f) the Cesro means of order of the Fourier-Laplace series of . The special value :=n22 of is known as the critical index. In the case when n is even, this paper proves the existence of the rare sequence {n k } such that the summability 1Nk=1Nnk(f)(x)f(x),N takes place at each Lebesgue point satisfying some antipole conditions.