Sharp weak bounds and limiting weak-type behavior for Hardy type operators

2018/04/02 by He, Qianjun, Yan, Dunyan
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.00460

Abstract

In this paper, Hardy type operator H_β on \bRⁿ and its adjoint operator H_β^* are investigated. We use novel methods to obtain two main results. One is that we obtain the operators H_β and H_β^* being bounded from L^p(|x|^α) to L^q,∞(|x|^γ), and the bounds of the operators H_β and H_β^* are sharp worked out. In particular, when α=γ=0, the norm of H_β is equal to 1. The other is that we study limiting weak-type behavior for the operator H_β and its optimal form was obtained.

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