The hilbert transform and maximal function for approximately homogeneous curves

Formula presented A homogeneous curve is one which satisfies a differential equation γ₁(t) — (A/t)γ₁{t), 0 < t < oo, where A is a nonsingular matrix all of whose eigenvalues have positive real part. An approximately homogeneous curve γ(t) has the form γ₁(0 + γ₂(0> where γ₂(t) is a carefully specified “error”, such that yfp is also restricted for j = 2, n + 1. The approximately homogeneous curves generalize the curves of standard type treated by Stein and Wainger.