Premium
Multilinear and multiparameter spectral multipliers on stratified groups
Author(s) -
Fang Jingxuan,
Zhao Jiman
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5082
Subject(s) - multilinear map , mathematics , nilpotent , multiplier (economics) , pure mathematics , lie group , economics , macroeconomics
As far as we know, the study of multilinear spectral multipliers on nilpotent Lie groups is a very new research work. There is even no study of Hörmander‐type multiplier theorem for multilinear and multiparameter spectral multipliers on nilpotent Lie groups. In this paper, on product spaces of stratified groups G = G 1 × ⋯ × G M , we prove Hörmander‐type multiplier theorems for multilinear and multiparameter spectral multipliers from L p 1( G ) × ⋯ × L p N( G ) to L r ( G ) with 1 ⩽ p 1 , ⋯ , p N , r ⩽ ∞ , fromLϖ 1p 1( G ) × ⋯ × Lϖ Np N( G ) toL ϖ r ( G ) with 1 < p 1 , ⋯ , p N , r ⩽ ∞ , and from L p 1 ( · ) ( G ) × ⋯ × L p N ( · ) ( G ) to L r (·) ( G ) with 1 < p ℓ − ⩽ p ℓ + ⩽ ∞ or 1 ⩽ p ℓ − ⩽ p ℓ + < ∞ for all ℓ = 1,…, N .