The multi-parameter Hausdorff operators on H¹ and L^p

2017/05/07 by Huy, Duong Quoc, Ky, Luong Dang
#47B38 (42B30) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.02548

Abstract

In the present paper, we characterize the nonnegative functions φ for which the multi-parameter Hausdorff operator \mathcal H_φ generated by φ is bounded on the multi-parameter Hardy space H¹(\mathbb R×⋯×\mathbb R) or L^p(\mathbb Rⁿ), p∈ [1,∞]. The corresponding operator norms are also obtained. Our results improve some recent results in \citeFZ, LM2, LM3, We and give an answer to an open question posted by Liflyand \citeLi.

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