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Hausdorff type operators on the power weighted Hardy spaces H | · | α p ( R n )
Author(s) -
Ruan Jianmiao,
Fan Dashan
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600257
Subject(s) - mathematics , hausdorff space , hardy space , type (biology) , bounded function , hausdorff measure , hausdorff distance , pure mathematics , operator (biology) , mathematical analysis , hausdorff dimension , ecology , biochemistry , chemistry , repressor , gene , transcription factor , biology
In this paper, we study the high‐dimensional Hausdorff type operators and establish their boundedness on the power weighted Hardy spacesH | · | α p ( R n )for 0 < p < 1 . As a consequence, we obtain that the Hausdorff type operator H Φ is bounded onH | · | α p ( R n )if Φ is the Gauss function, or the Poisson function.