International Congress of Mathematicians

Singular Integrals Aleet Modulation Invariance725Ci V.Figure 2: "Circles"derivative of m can by translated to a point far away from the origin, until the valueof the derivative, which remains constant at the translated points, contradicts (1.9).A natural replacement for (1.9) in the presence of modulation symmetry alongvectors in F has been introduced by Gilbert/Nahmod [6]:ll Pj-We remark that it is unknown whether the condition dim(F) < n/2 can berelaxed in this theorem.The forms A have dual multilinear operators. Theorem 2.1 implies a prioriestimates for these multilinear operators. Aloreover, these multilinear operatorssatisfy estimates which cannot be formulated in terms of IP estimates for A. Let(pi,..., p n ) bea tuple of real numbers or oo such that at most one of these numbers