Sobolev inequalities via Muramatu's integral formula
Abstract
For the Sobolev space Wmp(Rn) with positive integer m and 1<p<infty, sometimes replaced by 1<=p<infty, we consider the case m-n/p<0 and the case m-n/p=0, and give new proofs of the Sobolev embedding theorems by Muramatu's integral formula. When m-n/p<0, the embedding into Lq(Rn) with q satisfying m-n/p=-n/q is derived without the Hardy-Littlewood-Sobolev inequality by incorporating the method to prove it. When m-n/p=0, we prove the embedding into the BMO space or the VMO space as well as Trudinger's inequality.
Copyright (c) 2019 Yoichi Miyazaki
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
