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Cesàro-type operators on average radial integrability spaces induced by doubling weights
Abstract
In this paper, we study the Cesàro-type operator Cesμ,βf(z)=∫[0,1)f(tz)/((1−tz)β) dμ(t), where μ is a positive Borel measure on [0,1) and β>0. For 0<p,q<∞ and radial doubling weights ω1,ω2, we prove that Cesμ,β:ALpq(ω1)→ALpq(ω2) is bounded if and only if μ([0,1))+sup1/2≤ r<1μ([r,1))/((1−r)β)(whatω2(r)/whatω1(r))1/p<∞, and its norm is comparable to this quantity. For standard weights, our result extends \cite{BlascoMas2026,GalanopoulosSiskakisZhao2025} to the full range 0<p=q<∞. We further characterize compactness and the essential norm on average radial integrability spaces induced by doubling weights.
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BibTeX
@misc{pan2026cesàrotype,
title = {{Cesàro-type operators on average radial integrability spaces induced by doubling weights}},
author = {Jiaxin Pan and Cezhong Tong and Zixing Yuan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24216},
eprint = {2609.24216},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24216},
}
RIS
TY - UNPB
TI - Cesàro-type operators on average radial integrability spaces induced by doubling weights
AU - Jiaxin Pan
AU - Cezhong Tong
AU - Zixing Yuan
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24216
UR - https://arxiv.org/abs/2609.24216
AB - In this paper, we study the Cesàro-type operator Ces_μ,βf(z)=∫_[0,1)f(tz)/((1−tz)^β) dμ(t), where μ is a positive Borel measure on [0,1) and β>0. For 0<p,q<∞ and radial doubling weights ω_1,ω_2, we prove that Ces_μ,β:AL_p^q(ω_1)→AL_p^q(ω_2) is bounded if and only if μ([0,1))+sup_1/2≤ r<1μ([r,1))/((1−r)^β)(whatω_2(r)/whatω_1(r))^1/p<∞, and its norm is comparable to this quantity. For standard weights, our result extends \cite{BlascoMas2026,GalanopoulosSiskakisZhao2025} to the full range 0<p=q<∞. We further characterize compactness and the essential norm on average radial integrability spaces induced by doubling weights.
ER -