10 papers
The weak-type (1,1) bound for the Hardy--Littlewood maximal function is
Daniel Spector, Cody B. Stockdale
We prove a weak-type estimate for the centered Hardy--Littlewood maximal function with respect to Euclidean balls with dimensional dependence . This imp…
A dimension-free weak-type bound for the vector Riesz transform on
Yuyuan Ouyang, Daniel Spector, Cody B. Stockdale
We show that the best constant in the weak-type bound for the vector Riesz transform on is at most , independent of the dimension . The proof relies on…
An atomic decomposition for functions of bounded variation
Daniel Spector, Cody B. Stockdale, Dmitriy Stolyarov
In this paper, we give a decomposition of the gradient measure of an arbitrary function of bounded variation into a sum of atoms , where is a set of finite p…
On the Fourier transform of measures in Besov spaces
Riju Basak, Daniel Spector, Dmitriy Stolyarov
We prove quantitative estimates for the decay of the Fourier transform of the Riesz potential of measures that are in homogeneous Besov spaces of negative exponent: \begin{align*}…
An atomic decomposition of one-dimensional metric currents without boundary
You-Wei Benson Chen, Jesse Goodman, Felipe Hernandez +1
This paper proves an atomic decomposition of the space of -dimensional metric currents without boundary, in which the atoms are specified by closed Lipschitz curves with uniform…
A sparse resolution of the DiPerna-Majda gap problem for D Euler equations
Oscar Domínguez, Daniel Spector
A central question which originates in the celebrated work in the 1980's of DiPerna and Majda asks what is the optimal decay such that uniform rates of…
and gradient estimates for solutions of critical elliptic equations
You-Wei Benson Chen, Juan Manfredi, Daniel Spector
In this paper we explore several applications of the recently introduced spaces of functions of bounded -dimensional mean oscillation for to regularity theory of cr…
Potential trace inequalities via a Calderón-type theorem
Zdeněk Mihula, Luboš Pick, Daniel Spector
In this paper we develop a general theoretical tool for the establishment of the boundedness of notoriously difficult operators (such as potentials) on certain specific types of re…
On dimension stable spaces of measures
Daniel Spector, Dmitriy Stolyarov
In this paper, we define spaces of measures with dimensional stability . These spaces bridge between , the space of finite Radon…
On the Trace of
Giovanni Leoni, Daniel Spector
In this paper we prove extension results for functions in Besov spaces. Our results are new in the homogeneous setting, while our technique applies equally in the inhomogeneous set…