TY - JOUR
T1 - Endpoint L1 estimates for Hodge systems
AU - Hernandez, Felipe
AU - Raiță, Bogdan
AU - Spector, Daniel
N1 - Funding Information:
The authors would like to thank Dima Stolyarov for his comments on an early draft of the manuscript, as well as the referees for their careful reading and comments. F.H. is supported by the Fannie & John Hertz Foundation. D. S. is supported by the Taiwan Ministry of Science and Technology under research Grant number 110-2115-M-003-020-MY3 and the Taiwan Ministry of Education under the Yushan Fellow Program. Part of this work was undertaken while D. S. was visiting the National Center for Theoretical Sciences in Taiwan. He would like to thank the NCTS for its support and warm hospitality during the visit.
Funding Information:
The authors would like to thank Dima Stolyarov for his comments on an early draft of the manuscript, as well as the referees for their careful reading and comments. F.H. is supported by the Fannie & John Hertz Foundation. D. S. is supported by the Taiwan Ministry of Science and Technology under research Grant number 110-2115-M-003-020-MY3 and the Taiwan Ministry of Education under the Yushan Fellow Program. Part of this work was undertaken while D. S. was visiting the National Center for Theoretical Sciences in Taiwan. He would like to thank the NCTS for its support and warm hospitality during the visit.
Publisher Copyright:
© 2022, The Author(s).
PY - 2023/4
Y1 - 2023/4
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.
UR - http://www.scopus.com/inward/record.url?scp=85127268732&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85127268732&partnerID=8YFLogxK
U2 - 10.1007/s00208-022-02383-y
DO - 10.1007/s00208-022-02383-y
M3 - Article
AN - SCOPUS:85127268732
SN - 0025-5831
VL - 385
SP - 1923
EP - 1946
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3-4
ER -