Essential norm estimates for multilinear singular and fractional integrals

Alexander Meskhi. "Essential norm estimates for multilinear singular and fractional integrals." Commentationes Mathematicae 59.1-2 (2019): null. <http://eudml.org/doc/295467>.

@article{AlexanderMeskhi2019,
abstract = {We derive lower two-weight estimates for the essential norm (measure of noncompactness) for multilinear Hilbert and Riesz transforms, and Riesz potential operators in Banach function lattices. As a corollary we have appropriate results in weighted Lebesgue spaces. From these statements we conclude that there is no $(m+1)$-tuple of weights $(v,w_1, \dots , w_m)$ for which these operators are compact from $L^\{p_1\}_\{w_1\} \times \dots \times L^\{p_m\}_\{w_m\}$ to $L^q_v$.},
author = {Alexander Meskhi},
journal = {Commentationes Mathematicae},
keywords = {Multilinear Hilbert and Riesz transforms; multilinear fractional integrals; measure of noncompactness; weighted inequalities; Banach function lattices},
language = {eng},
number = {1-2},
pages = {null},
title = {Essential norm estimates for multilinear singular and fractional integrals},
url = {http://eudml.org/doc/295467},
volume = {59},
year = {2019},
}

TY - JOUR
AU - Alexander Meskhi
TI - Essential norm estimates for multilinear singular and fractional integrals
JO - Commentationes Mathematicae
PY - 2019
VL - 59
IS - 1-2
SP - null
AB - We derive lower two-weight estimates for the essential norm (measure of noncompactness) for multilinear Hilbert and Riesz transforms, and Riesz potential operators in Banach function lattices. As a corollary we have appropriate results in weighted Lebesgue spaces. From these statements we conclude that there is no $(m+1)$-tuple of weights $(v,w_1, \dots , w_m)$ for which these operators are compact from $L^{p_1}_{w_1} \times \dots \times L^{p_m}_{w_m}$ to $L^q_v$.
LA - eng
KW - Multilinear Hilbert and Riesz transforms; multilinear fractional integrals; measure of noncompactness; weighted inequalities; Banach function lattices
UR - http://eudml.org/doc/295467
ER -