PreprintCC BY 4.0arXiv
Carleson measures, Volterra integral operators and multipliers for QK spaces
Abstract
We study embeddings and operators on the Möbius-invariant spaces QK using two dyadic capacities. One capacity is defined by analytic packets; the other is defined by domination of positive semidefinite matrices. We prove that they are equivalent. They give criteria for bounded and compact embeddings QK→ L2(μ), bounded and compact Volterra operators, and pointwise multipliers. For the weights K(t)=tp/logβ(e/t), 0<p<1 and β≥1, we prove ℳ(QK)subsetneq H∞∩ QKlog. This disproves the logarithmic multiplier conjecture recorded in Bao and Wulan's 2021 survey.
Related
- Carleson Measures and Integral Operators on Fock--Sobolev Spaces
- Dunkl--BMO functions representable in terms of generalized balayage of Carleson measures and an application
- Littlewood-Paley and Carleson measure characterizations of Lipschitz spaces adapted to Schrödinger operators
- Homogeneous Polynomial Carleson Operators Along the Paraboloid
- Volterra Integral Reduction for Boundary Diffusion Problems
BibTeX
@misc{cao2026carleson,
title = {{Carleson measures, Volterra integral operators and multipliers for $Q_K$ spaces}},
author = {Wujun Cao and Zhouyuan Jiang and Songxiao Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.20205},
eprint = {2608.20205},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20205},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Carleson measures, Volterra integral operators and multipliers for Q_K spaces
AU - Wujun Cao
AU - Zhouyuan Jiang
AU - Songxiao Li
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2608.20205
UR - https://arxiv.org/abs/2608.20205
AB - We study embeddings and operators on the Möbius-invariant spaces Q_K using two dyadic capacities. One capacity is defined by analytic packets; the other is defined by domination of positive semidefinite matrices. We prove that they are equivalent. They give criteria for bounded and compact embeddings Q_K→ L^2(μ), bounded and compact Volterra operators, and pointwise multipliers. For the weights K(t)=t^p/log^β(e/t), 0<p<1 and β≥1, we prove ℳ(Q_K)subsetneq H^∞∩ Q_K^log. This disproves the logarithmic multiplier conjecture recorded in Bao and Wulan's 2021 survey.
ER -