摘要
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 Lp(G, xα) to Lq(G, xβ), 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.
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 Lp（G, xα） to Lq（G, xβ）, 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.
基金
supported by National Natural Science Foundation of China (Grant Nos.11071250 and 10931001)
