TY - JOUR
T1 - Multilinear paraproducts on Sobolev spaces
AU - Di Plinio, Francesco
AU - Green, A. Walton
AU - Wick, Brett D.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Unione Matematica Italiana 2024.
PY - 2025/3
Y1 - 2025/3
N2 - Paraproducts are a special subclass of the multilinear Calderón-Zygmund operators, and their Lebesgue space estimates in the full multilinear range are characterized by the BMO norm of the symbol. In this note, we characterize the Sobolev space boundedness properties of multilinear paraproducts in terms of a suitable family of Triebel-Lizorkin type norms of the symbol. Coupled with a suitable wavelet representation theorem, this characterization leads to a new family of Sobolev space T(1)-type theorems for multilinear Calderón-Zygmund operators.
AB - Paraproducts are a special subclass of the multilinear Calderón-Zygmund operators, and their Lebesgue space estimates in the full multilinear range are characterized by the BMO norm of the symbol. In this note, we characterize the Sobolev space boundedness properties of multilinear paraproducts in terms of a suitable family of Triebel-Lizorkin type norms of the symbol. Coupled with a suitable wavelet representation theorem, this characterization leads to a new family of Sobolev space T(1)-type theorems for multilinear Calderón-Zygmund operators.
KW - Multilinear Calderón-Zygmund theory
KW - Paraproducts
KW - Sobolev spaces
KW - Sparse domination
KW - Triebel-Lizorkin norms
KW - Wavelet representation theorem
UR - https://www.scopus.com/pages/publications/85208955162
U2 - 10.1007/s40574-024-00444-5
DO - 10.1007/s40574-024-00444-5
M3 - Article
AN - SCOPUS:85208955162
SN - 1972-6724
VL - 18
SP - 167
EP - 183
JO - Bollettino dell'Unione Matematica Italiana
JF - Bollettino dell'Unione Matematica Italiana
IS - 1
ER -