Sharp weak bounds for n-dimensional fractional Hardy operators

Abstract

We obtain the operator norms of the n-dimensional fractional Hardy operator {{\displaystyle H}}_{\alpha }(\mathrm{0}\langle \alpha \langle N) from weighted Lebesgue spaces {{\displaystyle L}}_{{\left|x\right|}^p}^p({ℝ}^n) to weighted weak Lebesgue spaces {{\displaystyle L}}_{{\left|x\right|}^{\beta }}^{q,\infty }({ℝ}^n).

Key words： Sharp weak bound; fractional Hardy operator; Lebesgue space with power weight

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