Resumen de Generic trilinear multipliers associated to degenerate simplexes

Robert Kesler

• For each 1≤?≤∞ , let ??(ℝ)={?∈??(ℝ):?̂ ∈??′(ℝ)} be equipped with the norm ||?||??(ℝ)=∣∣|?̂ ∣∣|??′(ℝ) . Moreover, let ?1,?2:ℝ2→ℂ satisfy the condition that for all ?∈ℤ2≥0 there is ??1,?2,?>0 such that for all ?∈ℝ2 and ?∈{1,2} , ∣∣∂???(?)∣∣≤??1,?2,?????(?,?)|?| . Our main result is that the trilinear multiplier given on (ℝ)3 by ?[?1,?2]:(?1,?2,?3)↦∫ℝ3?1(?1,?2)?2(?2,?3)[∏?=13??^(??)?2?????]??1??2??3 extends to a bounded map from ??1(ℝ)×??2(ℝ)×??3(ℝ) into ?11?1+1?2+1?3(ℝ) provided 1