35 citations · 165 across the 26 of their papers we have counts for
38 papers
Capacitary Maximal Inequalities and Applications
You-Wei Benson Chen, Keng Hao Ooi, Daniel Spector
In this paper we introduce capacitary analogues of the Hardy-Littlewood maximal function, \begin{align*} \mathcal{M}_C(f)(x):= \sup_{r>0} \frac{1}{C(B(x,r))} \int_{B(x,r)} |f|\;dC,…
Some Remarks on Capacitary Integrals and Measure Theory
Augusto C. Ponce, Daniel Spector
We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and stro…
On functions of bounded -dimensional mean oscillation
You-Wei Benson Chen, Daniel Spector
In this paper, we define a notion of -dimensional mean oscillation of functions which are integrable on -dimensional subsets of t…
A trace inequality for solenoidal charges
Bogdan Raita, Daniel Spector, Dmitriy Stolyarov
We prove that for , one has the trace inequality \begin{align*} \int_{\mathbb{R}^d} |I_αF| \;dν\leq C |F|(\mathbb{R}^d)\|ν\|_{\mathcal{M}^{d-α}(\mathbb{R}^d)} \end{al…
The fractional variation and the precise representative of functions
Giovanni E. Comi, Daniel Spector, Giorgio Stefani
We continue the study of the fractional variation following the distributional approach developed in the previous works arXiv:1809.08575, arXiv:1910.13419 and arXiv:2011.03928. We…
Endpoint estimates for Hodge systems
Felipe Hernandez, Bogdan Raita, Daniel Spector
In this paper we give a simple proof of the endpoint Besov-Lorentz estimate $$ \|I_αF\|_{\dot{B}^{0,1}_{d/(d-α),1}(\mathbb{R}^d;\mathbb{R}^k)} \leq C \|F \|_{L^1(\mathbb{R}^d;\math…