TY - JOUR
T1 - Higher-order interpolation inequalities with weights for radial functions
AU - Takada, Ryo
AU - Yoneda, Keiji
N1 - Funding Information:
The authors would like to express their great thanks to Professor Hidemitsu Wadade for valuable advices and fruitful discussions. The authors would like to thank the referees for constructive suggestions. This work was supported by JSPS KAKENHI Grant Numbers JP19K03584 , JP18KK0072 , JP17H02851 and JP20H01814 .
Publisher Copyright:
© 2020 Elsevier Ltd
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2021/2
Y1 - 2021/2
N2 - We consider higher-order interpolation inequalities of the Gagliardo–Nirenberg type with power weights for radial functions. We show that those inequalities hold for a better range of admissible power weights if we restrict ourselves to the space of radially symmetric functions. The key of the proof is to reduce the problem to a radial improvement for the weighted Hardy–Littlewood–Sobolev inequalities.
AB - We consider higher-order interpolation inequalities of the Gagliardo–Nirenberg type with power weights for radial functions. We show that those inequalities hold for a better range of admissible power weights if we restrict ourselves to the space of radially symmetric functions. The key of the proof is to reduce the problem to a radial improvement for the weighted Hardy–Littlewood–Sobolev inequalities.
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U2 - 10.1016/j.na.2020.112158
DO - 10.1016/j.na.2020.112158
M3 - Article
AN - SCOPUS:85092203692
VL - 203
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
M1 - 112158
ER -