Generic trilinear multipliers associated to degenerate simplexes

• Autores: Robert Kesler
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 70, Fasc. 1, 2019, págs. 153-186
• Idioma: inglés
• DOI: 10.1007/s13348-018-0224-z
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• Resumen

  • 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