@article{oai:kanazawa-u.repo.nii.ac.jp:00043295,
 author = {佐藤, 秀一 and Sato, Shuichi and Wang, F. and Yang, D. and Yuan, W.},
 issue = {07},
 journal = {Communications in Contemporary Mathematics},
 month = {Oct},
 note = {In this paper, the authors characterize the Sobolev spaces (Formula presented.) with (Formula presented.) and (Formula presented.) via a generalized Lusin area function and its corresponding Littlewood–Paley (Formula presented.)-function. The range (Formula presented.) is also proved to be nearly sharp in the sense that these new characterizations are not true when (Formula presented.) and (Formula presented.). Moreover, in the endpoint case (Formula presented.), the authors also obtain some weak type estimates. Since these generalized Littlewood–Paley functions are of wide generality, these results provide some new choices for introducing the notions of fractional Sobolev spaces on metric measure spaces. © 2017 World Scientific Publishing Company, Embargo Period 12 months, 金沢大学人間社会研究域学校教育系},
 title = {Generalized Littlewood–Paley characterizations of fractional Sobolev spaces},
 volume = {20},
 year = {2017}
}