6 papers · 1 filter
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…
A Remark on an Integral Characterization of the Dual of BV
Nicola Fusco, Daniel Spector
In this paper, we show how under the continuum hypothesis one can obtain an integral representation for elements of the topological dual of the space of functions of bounded variat…
On a new class of fractional partial differential equations II
Daniel Spector, Tien-Tsan Shieh
In this paper we continue to advance the theory regarding the Riesz fractional gradient in the calculus of variations and fractional partial differential equations begun in an earl…
A Leray-Trudinger Inequality
Georgios Psaradakis, Daniel Spector
We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case In this paper we provide an optimal Sobolev-type…
-Taylor approximations characterize the Sobolev space
Daniel E. Spector
In this note, we introduce a variant of Calderón and Zygmund's notion of -differentiability - an \emph{-Taylor approximation}. Our first result is that functions in the S…