Strong Convergence of Spherical Harmonic Expansions on H 1 ( S d − 1 )
نویسنده
چکیده
Abstract. Let σ δ k denote the Cesàro means of order δ > −1 of the spherical harmonic expansions on the unit sphere Sd−1, and let Ej ( f, H1) denote the best approximation of f in the Hardy space H1(Sd−1) by spherical polynomials of degree at most j . It is known that λ := (d −2)/2 is the critical index for the summability of the Cesàro means on H1(Sd−1). The main result of this paper states that, for f ∈ H1(Sd−1),
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