PreprintCC BY 4.0arXiv
Weighted Hp−Lq boundedness of integral operators with rough kernels
Abstract
In this paper, we study integral operators Tαf(x)=∫ℝnK(x,y) f(y)dy, with kernels K(x,y)= k1( x− A1y)...km( x−Amy), where ki(x)=Ωi(x)/|x|n/qi and Ωi: ℝn→ ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, Ai are certain invertible matrices, and n/q1+…+n/qm=n−α, 0≤ α<n. We obtain the Hpwp(ℝn)−Lqwq(ℝn) boundedness of these operators, for a class of Muckenhoupt weights w, satisfying the condition w(Aix)≤ cw(x), $a.e.x\in\mathbb{R} ^n $, 1≤ i≤ m.
Related
- Weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels
- Weak type (1,1) bound criterion for maximal truncated singular integral operators with rough kernels
- Multilinear rough singular integral operators may not be of the weak type at the endpoint
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- Weak Endpoint Estimate for Commutators of Rough Maximal Singular Integral operators
BibTeX
@misc{gallo2026weighted,
title = {{Weighted $H^p-L^q$ boundedness of integral operators with rough kernels}},
author = {Andrea L. Gallo and M. Silvina Riveros and Lucas A. Vallejos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.03567},
eprint = {2607.03567},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.03567},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weighted H^p−L^q boundedness of integral operators with rough kernels
AU - Andrea L. Gallo
AU - M. Silvina Riveros
AU - Lucas A. Vallejos
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2607.03567
UR - https://arxiv.org/abs/2607.03567
AB - In this paper, we study integral operators T_αf(x)=∫_ℝ^nK(x,y) f(y)dy, with kernels K(x,y)= k_1( x− A_1y)...k_m( x−A_my), where k_i(x)=Ω_i(x)/|x|^n/q_i and Ω_i: ℝ^n→ ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A_i are certain invertible matrices, and n/q_1+…+n/q_m=n−α, 0≤ α<n. We obtain the H^p_w^p(ℝ^n)−L^q_w^q(ℝ^n) boundedness of these operators, for a class of Muckenhoupt weights w, satisfying the condition w(A_ix)≤ cw(x), $a.e.x\in\mathbb{R} ^n $, 1≤ i≤ m.
ER -