Optimal Hardy Inequality for Fractional Laplacians on the Integers

We study the fractional Hardy inequality on the integers. We prove the optimality of the Hardy weight presented by Ciaurri/Roncal and hence affirmatively answer the question of sharpness of the constant.

(The thesis just provides criticality of the Hardy weight (which also already shows sharpness of the constant). We were now able to show that the weight is also null-critical, i.e., there is no minimizer, and is thus optimal. We are furthermore at the final stages of making this result publishable.)