Approximation by Boolean Sums of Jackson Operators on the Sphere
This paper discusses the approximation by the r-th Boolean sum of Jackson operators on the unit sphere S(n-1), circle plus(r) J(k,s)(f), including direct and inverse theorem as well as the saturation. Namely, we prove that there are constants C(1) and C(2) such that C(1) parallel to circle plus(r) J(k,s)f - f parallel to(p)  = k) parallel to circle plus(r) J(k,s)f - f parallel to(p) for any positive integer k and any p-th Lebesgue integrable function f de ned on the sphere, where omega(2r)(f, t)(p) is the modulus of smoothness of degree 2r of f. We also obtain that the saturation order for circle plus(r) J(k,s) is k(-2r).
approximation boolean sums jackson operators sphere saturation