COUPLING BY REFLECTION AND HOLDER REGULARITY FOR NON-LOCAL OPERATORS OF VARIABLE ORDER

doi:10.1090/tran/7259

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	COUPLING BY REFLECTION AND HOLDER REGULARITY FOR NON-LOCAL OPERATORS OF VARIABLE ORDER
	Luo, Dejun1,2 ; Wang, Jian 3,4
刊名	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
	2019
卷号	371 期号:1 页码:431-459
关键词	Stable-like process non-local operator Holder continuity coupling by reflection jump process
ISSN号	0002-9947
DOI	10.1090/tran/7259
英文摘要	We consider the non-local operator of variable order as follows: Lf(x) = integral(Rd\{0}) (f(x+z) - f(x) - del f(x), z 1{vertical bar z vertical bar <= 1})n(x,z)/vertical bar z vertical bar(d+alpha(x)) dz, where alpha(x) is an element of [alpha(0), alpha(2)] for any x is an element of R-d and some constants 0 < alpha(0) <= alpha(2) < 2 and n(x, z) is a positive Borel measurable function bounded from above and below. Under mild continuity conditions on alpha(x) and n(x, z), we establish the Holder regularity for the associated semigroups. The proof is based on a new construction of the coupling by reflection for non-local operator L, and the results successfully apply to both stable-like processes in the sense of Bass and time-change of symmetric stable processes.
资助项目	National Natural Science Foundation of China[11431014] ; National Natural Science Foundation of China[11571347] ; National Natural Science Foundation of China[11522106] ; Youth Innovation Promotion Association CAS[2017003] ; Special Talent Program of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences ; Fok Ying Tung Education Foundation[151002] ; National Science Foundation of Fujian Province[2015J01003] ; Program for Probability and Statistics: Theory and Application[IRTL1704]
WOS研究方向	Mathematics
语种	英语
出版者	AMER MATHEMATICAL SOC
WOS记录号	WOS:000452652400015
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/31836]
专题	应用数学研究所
通讯作者	Luo, Dejun
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Random Complex Struct & Data Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Fujian Normal Univ, Coll Math & Informat, Fuzhou 350007, Fujian, Peoples R China 4.Fujian Normal Univ, Fujian Key Lab Math Anal & Applicat FJKLMAA, Fuzhou 350007, Fujian, Peoples R China
推荐引用方式 GB/T 7714	Luo, Dejun,Wang, Jian. COUPLING BY REFLECTION AND HOLDER REGULARITY FOR NON-LOCAL OPERATORS OF VARIABLE ORDER[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2019,371(1):431-459.
APA	Luo, Dejun,&Wang, Jian.(2019).COUPLING BY REFLECTION AND HOLDER REGULARITY FOR NON-LOCAL OPERATORS OF VARIABLE ORDER.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,371(1),431-459.
MLA	Luo, Dejun,et al."COUPLING BY REFLECTION AND HOLDER REGULARITY FOR NON-LOCAL OPERATORS OF VARIABLE ORDER".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 371.1(2019):431-459.