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Weighted Norm Inequalities for Maximal Multi-sublinear Rough Singular Integrals
Abstract
We continue our study of multilinear rough homogeneous singular integrals by establishing weighted estimates for their maximal truncations. Let m≥2 and let Ω∈ Lq(𝕊mn−1), 1<q≤∞, have mean zero. For 1<p1,…,pm<∞ with pj≥ q' and 1/p=∑j=1m1/pj, we prove ‖ ℒΩ*(f1,…,fm)‖Lp(vw⃗) ≲ ‖Ω‖Lq(𝕊mn−1) ∏j=1m‖ fj‖Lpj(wj) whenever w⃗=(w1,…,wm)∈ A(p1/q',…,pm/q'), where q' is the Hölder conjugate of q and vw⃗=∏j=1m wjp/pj. The estimate holds under the same multiple weight condition as the corresponding principal value estimate.
Related
- SPARSE POINTWISE BOUNDS FOR MAXIMAL TRUNCATIONS OF ROUGH SINGULAR INTEGRALS AND SOBOLEV-TYPE INEQUALITIES
- Weak type (1,1) estimates for noncommutative maximal truncated rough singular integrals
- Maximal directional singular integrals
- Sparse bounds for maximal rough singular integrals
- Sharp weighted weak-type bounds for commutators of singular integrals
BibTeX
@misc{park2026weighted,
title = {{Weighted Norm Inequalities for Maximal Multi-sublinear Rough Singular Integrals}},
author = {Bae Jun Park},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18296},
eprint = {2610.18296},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18296},
}
RIS
TY - UNPB
TI - Weighted Norm Inequalities for Maximal Multi-sublinear Rough Singular Integrals
AU - Bae Jun Park
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18296
UR - https://arxiv.org/abs/2610.18296
AB - We continue our study of multilinear rough homogeneous singular integrals by establishing weighted estimates for their maximal truncations. Let m≥2 and let Ω∈ L^q(𝕊^mn−1), 1<q≤∞, have mean zero. For 1<p_1,…,p_m<∞ with p_j≥ q' and 1/p=∑_j=1^m1/p_j, we prove ‖ ℒ_Ω^*(f_1,…,f_m)‖_L^p(v_w⃗) ≲ ‖Ω‖_L^q(𝕊^mn−1) ∏_j=1^m‖ f_j‖_L^p_j(w_j) whenever w⃗=(w_1,…,w_m)∈ A_(p_1/q',…,p_m/q'), where q' is the Hölder conjugate of q and v_w⃗=∏_j=1^m w_j^p/p_j. The estimate holds under the same multiple weight condition as the corresponding principal value estimate.
ER -