GEOMETRY OF FOURIER TRANSFORMS AND RESTRICTION THEOREMS.

摘要

We say that a restriction theorem holds for a curve (gamma) (t) in (//R)('n) if for all f(epsilon) ((//R)('n)) and for some p and q, there is a constant C(,p,q) such that.;In Chapter 1, we prove restriction theorems for non-compact plane curves with non-negative affine curvature when 1 (LESSTHEQ) p < 4/3 and.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;There is an analogous result for space curves in the same chapter.;(VBAR)(VBAR) f (VBAR) (,(gamma)) (VBAR)(VBAR) (,L('q)(du)) (LESSTHEQ) C(,p,q) (VBAR)(VBAR) f (VBAR)(VBAR) (,L('P)((//R)('n))).;The Hilbert transform along the curve (gamma) is defined by.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;In Chapter 2, it is shown that when (gamma) has the rapidly decreasing positive affine curvature, H(,(gamma)) is a L('P)-bounded operator for.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).