摘要
Let S^(d-1) = {x : |x| = 1} be a unit sphere of the d-dimensional Euclideanspace R^d and let H^p = H^p(S^(d-1)) (0 < p ≤ 1) denote the real Hardy space on S^(d-1). For 0 < p≤ 1 and f ∈ H^p(S^(d-1)), let E_j (f, H^p) (j =0,1,...) be the best approximation of f byspherical polynomials of degree less than or equal to j, in the space H^p(S^(d-1)). Given adistribution f on S^(d-1), its Cesaro mean of order δ > -1 is denoted by σ_k~δ(f). For 0 < p ≤1, it is known that δ(p) := (d-1)/p - d/2 is the critical index for the uniform summability ofσ_k~δ(f) in the metric H^p.
Let S^(d-1) = {x : |x| = 1} be a unit sphere of the d-dimensional Euclideanspace R^d and let H^p = H^p(S^(d-1)) (0 < p ≤ 1) denote the real Hardy space on S^(d-1). For 0 < p≤ 1 and f ∈ H^p(S^(d-1)), let E_j (f, H^p) (j =0,1,...) be the best approximation of f byspherical polynomials of degree less than or equal to j, in the space H^p(S^(d-1)). Given adistribution f on S^(d-1), its Cesaro mean of order δ > -1 is denoted by σ_k~δ(f). For 0 < p ≤1, it is known that δ(p) := (d-1)/p - d/2 is the critical index for the uniform summability ofσ_k~δ(f) in the metric H^p.
基金
The authors are partially supported by NNSF of China under the grant#10071007
