Daniel Spector

Training Shakespeare's Yes in the Era of No

Shakespeare · 2023-07-04 · 1 citations

What I explore in what follows is a theory of why my job has become more difficult in recent years – not impossible, and in some ways more rewarding because of new challenges, but simply more demanding. Why have I found myself with unprecedented vigilance upholding certain virtues of Shakespeare before a student cohort reflexively suspicious of those virtues? Why has there seemed to be, more than ever before, a barrier to the kinds of interpersonal generosity that Shakespeare’s plays demand of a…

Estimates for the wave equation on $β$-dimensional spaces of measures

ArXiv.org · 2025-12-14

In this paper, we establish Miyachi-Peral-type fixed-time estimates for wave multipliers acting on $β$-dimension stable spaces of measures. Our estimates give a refinement of known estimates for the Hardy space. From these bounds, we deduce corresponding estimates for the wave equation with measure data.

The Capacitary John-Nirenberg Inequality Revisited

ArXiv.org · 2025-01-20

In this paper, we establish maximal function estimates, Lebesgue differentiation theory, Calderón-Zygmund decompositions, and John-Nirenberg inequalities for translation invariant Hausdorff contents. We further identify a key structural component of these results -- a packing condition satisfied by these Hausdorff contents which compensates for the non-linearity of the capacitary integrals. We prove that for any outer capacity, this packing condition is satisfied if and only if the capacity is e…

An atomic decomposition of one-dimensional metric currents without boundary

ArXiv.org · 2025-02-14

This paper proves an atomic decomposition of the space of $1$-dimensional metric currents without boundary, in which the atoms are specified by closed Lipschitz curves with uniform control on their Morrey norms. Our argument relies on a geometric construction which states that for any $ε>0$ one can express a piecewise-geodesic closed curve as the sum of piecewise-geodesic closed curves whose total length is at most $(1+ε)$ times the original length and whose Morrey norms are each bounded by a…

On the Trace of $\dot W_{a}^{m+1,1}(\mathbb{R}_{+}^{n+1})$

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE · 2025-05-30