TY - JOUR

T1 - Counterexamples for multi-parameter weighted paraproducts

AU - Mozolyako, Pavel

AU - Psaromiligkos, Georgios

AU - Volberg, Alexander

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We build the plethora of counterexamples to bi-parameter two weight embedding theorems. Two weight one parameter embedding results (which is the same as results of boundedness of two weight classical paraproducts, or two weight Carleson embedding theorems) are well known since the works of Sawyer in the 80's. Bi-parameter case was considered by S. Y. A. Chang and R. Fefferman but only when underlying measure is Lebesgue measure. The embedding of holomorphic functions on bi-disc requires general input measure. In [9] we classified such embeddings if the output measure has tensor structure. In this note we give examples that without tensor structure requirement all results break down.

AB - We build the plethora of counterexamples to bi-parameter two weight embedding theorems. Two weight one parameter embedding results (which is the same as results of boundedness of two weight classical paraproducts, or two weight Carleson embedding theorems) are well known since the works of Sawyer in the 80's. Bi-parameter case was considered by S. Y. A. Chang and R. Fefferman but only when underlying measure is Lebesgue measure. The embedding of holomorphic functions on bi-disc requires general input measure. In [9] we classified such embeddings if the output measure has tensor structure. In this note we give examples that without tensor structure requirement all results break down.

UR - http://www.scopus.com/inward/record.url?scp=85095708176&partnerID=8YFLogxK

U2 - 10.5802/CRMATH.52

DO - 10.5802/CRMATH.52

M3 - Article

AN - SCOPUS:85095708176

VL - 358

SP - 529

EP - 534

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 5

ER -