Hausdorff type operators on the power weighted Hardy spaces     H    |  ·  |   α   p    (    R   n   ) | Zendy

Ruan Jianmiao | Zendy; Fan Dashan | Zendy

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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.

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