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Explicit constants for Hardy’s inequality with power weight on n-dimensional product spaces

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Abstract

In this paper, Hardy operator H on n-dimensional product spaces G = (0,∞)n and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient and necessary conditions for the operators H and H* being bounded from L p(G, x α) to L q(G, x β), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 < p = q < +∞, norms of the operators H and H* are obtained.

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Authors and Affiliations

  1. School of Mathematics Science, Heilongjiang University, Haerbin, 150080, China

    ShiMo Wang

  2. School of Mathematics, Graduate University, Chinese Academy of Sciences, Beijing, 100049, China

    ShiMo Wang & DunYan Yan

  3. School of Mathematics, Beijing Normal University, Beijing, 100875, China

    ShanZhen Lu

Authors
  1. ShiMo Wang
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  2. ShanZhen Lu
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  3. DunYan Yan
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Correspondence to DunYan Yan.

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Wang, S., Lu, S. & Yan, D. Explicit constants for Hardy’s inequality with power weight on n-dimensional product spaces. Sci. China Math. 55, 2469–2480 (2012). https://doi.org/10.1007/s11425-012-4453-4

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  • DOI: https://doi.org/10.1007/s11425-012-4453-4

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