Zobrazeno 1 - 10
of 305
pro vyhledávání: '"Spector Daniel"'
Autor:
Roychowdhury, Prasun, Spector, Daniel
The main results of this paper are the establishment of sharp constants for several families of critical Sobolev embeddings. These inequalities were pioneered by David R. Adams, while the sharp constant in the first order case is due to Andrea Cianch
Externí odkaz:
http://arxiv.org/abs/2411.00293
Autor:
Domínguez, Oscar, Spector, Daniel
A central question which originates in the celebrated work in the 1980's of DiPerna and Majda asks what is the optimal decay $f > 0$ such that uniform rates $|\omega|(Q) \leq f(|Q|)$ of the vorticity maximal functions guarantee strong convergence wit
Externí odkaz:
http://arxiv.org/abs/2409.02344
Autor:
Martínez Ángel D., Spector Daniel
Publikováno v:
Advances in Nonlinear Analysis, Vol 10, Iss 1, Pp 877-894 (2020)
It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate. While thes
Externí odkaz:
https://doaj.org/article/279dc17acadf4f25b38021512a7e4c98
In this paper we explore several applications of the recently introduced spaces of functions of bounded $\beta$-dimensional mean oscillation for $\beta \in (0,n]$ to regularity theory of critical exponent elliptic equations. We first show that functi
Externí odkaz:
http://arxiv.org/abs/2407.13884
We establish an approach to trace inequalities for potential-type operators based on an appropriate modification of an interpolation theorem due to Calder\'on. We develop a general theoretical tool for establishing boundedness of notoriously difficul
Externí odkaz:
http://arxiv.org/abs/2407.03986
Autor:
Spector, Daniel, Stolyarov, Dmitriy
In this paper, we define spaces of measures $DS_\beta(\mathbb{R}^d)$ with dimensional stability $\beta \in (0,d)$. These spaces bridge between $M_b(\mathbb{R}^d)$, the space of finite Radon measures, and $DS_d(\mathbb{R}^d)= \mathrm{H}^1(\mathbb{R}^d
Externí odkaz:
http://arxiv.org/abs/2405.10728
Autor:
Leoni, Giovanni, Spector, Daniel
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 setting to obtain new proofs of classical results. While our results incl
Externí odkaz:
http://arxiv.org/abs/2404.18342
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, \end{align*} for $C=$ the Hausdorff content or a Riesz capacity. For
Externí odkaz:
http://arxiv.org/abs/2305.19046
Autor:
Ponce, Augusto C., Spector, Daniel
Publikováno v:
Lenhart, Suzanne and Xiao, Jie. Potentials and Partial Differential Equations: The Legacy of David R. Adams, De Gruyter, 2023
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 strong subadditivity independent of regularity assumptions on the capacity
Externí odkaz:
http://arxiv.org/abs/2302.11847
Autor:
Chen, You-Wei Benson, Spector, Daniel
In this paper, we define a notion of $\beta$-dimensional mean oscillation of functions $u: Q_0 \subset \mathbb{R}^d \to \mathbb{R}$ which are integrable on $\beta$-dimensional subsets of the cube $Q_0$: \begin{align*} \|u\|_{BMO^{\beta}(Q_0)}:= \sup_
Externí odkaz:
http://arxiv.org/abs/2207.06979