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^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1923-1946
Number of pages	24
Journal	Mathematische Annalen
Volume	385
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-022-02383-y
Publication status	Published - 2023 Apr

ASJC Scopus subject areas

General Mathematics

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abstract = "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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AU - Spector, Daniel

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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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ER -

Endpoint L¹ estimates for Hodge systems

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