Approximation of Hardy space on the unit sphere

摘要

The authors discuss the boundedness and approximation properties of translation and mean operator on H~1(Σ) by the estimates of high degree difference on ultraspherical polynomials, atom decomposition and construct properties on sphere. Also the boundedness and approximation of linear means at all kinds of indexes on H~p(0 < p < 1) and the almost everywhere convergence of Cesaro means are established.