Open AccessBoundedness of multidimensional Hausdorff operators in 𝐻^{𝑝} spaces, 0<𝑝<1
Author(s) -
Elijah Liflyand,
Akihiko Miyachi
Publication year - 2018
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/7572
Subject(s) - algorithm , artificial intelligence , computer science
Sufficient conditions, of both smoothness and algebraic type, for the boundedness of multidimensional Hausdorff operators in Hardy spaces H p ( R n ) H^p (\mathbb {R}^n) , n ≥ 2 n\ge 2 , 0 > p > 1 0>p>1 , are given. Positive and negative examples illustrate all aspects of the behavior of such operators and reveal the special nature of the case p > 1 p>1 .