Endpoint L1 estimates for Hodge systems

Felipe Hernandez; Bogdan Raiță; Daniel Spector

doi:10.1007/s00208-022-02383-y

Endpoint L¹ estimates for Hodge systems

Felipe Hernandez, Bogdan Raiță, Daniel Spector^*

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

6 引文斯高帕斯（Scopus）

摘要

Let d≥ 2. In this paper we give a simple proof of the endpoint Besov-Lorentz estimate ‖IαF‖B˙d/(d-α),10,1(Rd;Rk)≤C‖F‖L1(Rd;Rk)for all F∈ L¹(R^d; R^k) which satisfy a first order cocancelling differential constraint, where α∈ (0 , d) and I_α is a Riesz potential. We show how this implies endpoint Besov–Lorentz estimates for Hodge systems with L¹ data via fractional integration for exterior derivatives.

原文	英語
頁（從 - 到）	1923-1946
頁數	24
期刊	Mathematische Annalen
卷	385
發行號	3-4
DOIs	https://doi.org/10.1007/s00208-022-02383-y
出版狀態	已發佈 - 2023 4月

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一般數學

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N2 - Let d≥ 2. In this paper we give a simple proof of the endpoint Besov-Lorentz estimate ‖IαF‖B˙d/(d-α),10,1(Rd;Rk)≤C‖F‖L1(Rd;Rk)for all F∈ L1(Rd; Rk) which satisfy a first order cocancelling differential constraint, where α∈ (0 , d) and Iα is a Riesz potential. We show how this implies endpoint Besov–Lorentz estimates for Hodge systems with L1 data via fractional integration for exterior derivatives.

AB - Let d≥ 2. In this paper we give a simple proof of the endpoint Besov-Lorentz estimate ‖IαF‖B˙d/(d-α),10,1(Rd;Rk)≤C‖F‖L1(Rd;Rk)for all F∈ L1(Rd; Rk) which satisfy a first order cocancelling differential constraint, where α∈ (0 , d) and Iα is a Riesz potential. We show how this implies endpoint Besov–Lorentz estimates for Hodge systems with L1 data via fractional integration for exterior derivatives.

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JO - Mathematische Annalen

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ER -

Endpoint L1 estimates for Hodge systems

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Endpoint L¹ estimates for Hodge systems