This article is devoted to the study of variable 2-microlocal Besov-type and Triebel- Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize t...This article is devoted to the study of variable 2-microlocal Besov-type and Triebel- Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize these spaces by means of Q-transforms, Peetre maximal functions, smooth atoms, ball means of differences and approximations by analytic functions. As applications, some re- lated Sobolev-type embeddings and trace theorems of these spaces are Mso established. Moreover, some obtained results, such as characterizations via approximations by analytic functions, are new even for the classical variable Besov and Triebel-Lizorkin spaces.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11571039,11671185,11471042 and 11701174)supported by the Construct Program of the Key Discipline in Hu’nan Province+1 种基金the Scientific Research Fund of Hu’nan Provincial Education Department(Grant No.17B159)the Scientific Research Foundation for Ph.D.Hu’nan Normal University(Grant No.531120-3257)
文摘This article is devoted to the study of variable 2-microlocal Besov-type and Triebel- Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize these spaces by means of Q-transforms, Peetre maximal functions, smooth atoms, ball means of differences and approximations by analytic functions. As applications, some re- lated Sobolev-type embeddings and trace theorems of these spaces are Mso established. Moreover, some obtained results, such as characterizations via approximations by analytic functions, are new even for the classical variable Besov and Triebel-Lizorkin spaces.
