Pointwise Estimates for a Class of Singular Integrals and Higher Commutators

<正> §Ⅰ. Pointwise and Weak-type Estimates Denote M（Rk）, M（Rk×Rk） as the space of Lebesque measurable functions defined on Rk, Rk×Rk, respectively. Let L: H→M（Rk×Rk） be a linear operator defined on H, which is a linearsubspace of M（Rk）. There exist the follwing conditions on L and H: i) If U is a convex open set in Rk, x, y∈U and a∈H, then xu·a∈H, and