The hilbert transform and maximal function for approximately homogeneous curves

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Abstract

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.

Original languageEnglish
JournalTransactions of the American Mathematical Society
Volume267
Issue number1
DOIs
StatePublished - 1981

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