Boundedness of Hausdorff operators on real Hardy spaces H1 over locally compact groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Mirotin, A. R.¹ 

[1] F Skorina Gomel State Univ, Dept Math & Programming Technol, Sovietskaya 104, Gomel 246019, BELARUS

关键词: Hausdorff operator;    Cesaro operator;    Hardy space;    Space of homogeneous type;    Homogeneous group;    Heisenberg group;   

DOI  :  10.1016/j.jmaa.2018.12.065

来源: Elsevier

【 摘 要 】

Results of Liflyand and collaborators on the boundedness of Hausdorff operators on the Hardy space H-1 over finite-dimensional real space are generalized to the case of locally compact groups that are spaces of homogeneous type. Special cases and examples of compact Lie groups, homogeneous groups (in particular the Heisenberg group) and finite-dimensional spaces over division rings are considered. In conclusion, we solve for the space L-2 an open question on compactness of a Hausdorff operator posed by Liflyand. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free