PreprintCC BY 4.0arXiv
Revisiting Positive Exponent power weighted Stein-Weiss inequalities in L1
Abstract
We obtain the necessary and sufficient conditions on input functions for a family of positive exponent power weight L1 Stein-Weiss inequalities. Earlier work by De Nápoli and Picon showed that a certain cocanceling condition was necessary and sufficient in L1, but it was unknown if this condition remained necessary in the positive exponent power weight setting. This present article identifies weaker necessary conditions for positive exponent power weights, some of which were shown to be sufficient for positive, non-integer exponent power weights in the author's earlier work.
Related
- Correction to the article "Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance"
- An Upper Bound to the Undetected Error Exponent with Erasure Decoding at Positive Rates
- Gradient Estimates Near the Natural Exponent for Very Weak Solutions to Ap-Weighted Quasilinear Elliptic Equations
- The Serrin exponent for Lane-Emden inequalities driven by sums of fractional p-Laplacians
- Rigidity of positive rupture solutions to a biharmonic equation with critical negative exponent
BibTeX
@misc{zhang2026revisiting,
title = {{Revisiting Positive Exponent power weighted Stein-Weiss inequalities in $L^1$}},
author = {Wen Qi Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11048},
eprint = {2610.11048},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11048},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Revisiting Positive Exponent power weighted Stein-Weiss inequalities in L^1
AU - Wen Qi Zhang
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11048
UR - https://arxiv.org/abs/2610.11048
AB - We obtain the necessary and sufficient conditions on input functions for a family of positive exponent power weight L^1 Stein-Weiss inequalities. Earlier work by De Nápoli and Picon showed that a certain cocanceling condition was necessary and sufficient in L^1, but it was unknown if this condition remained necessary in the positive exponent power weight setting. This present article identifies weaker necessary conditions for positive exponent power weights, some of which were shown to be sufficient for positive, non-integer exponent power weights in the author's earlier work.
ER -