Boundedness of multidimensional Hausdorff operators in 𝐻^{𝑝} spaces, 0<𝑝<1

Liflyand, Elijah; Miyachi, Akihiko

doi:10.1090/tran/7572

Boundedness of multidimensional Hausdorff operators in $H^p$ spaces, $0<p<1$
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Trans. Amer. Math. Soc. 371 (2019), 4793-4814 Request permission

Abstract:

Sufficient conditions, of both smoothness and algebraic type, for the boundedness of multidimensional Hausdorff operators in Hardy spaces $H^p (\mathbb {R}^n)$, $n\ge 2$, $0<p<1$, are given. Positive and negative examples illustrate all aspects of the behavior of such operators and reveal the special nature of the case $p<1$.

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