Related papers: $p$-capacity with Bessel convolution

In analogy with bilinear Riesz potentials, we introduce bilinear Bessel potentials and characterize their boundedness from $L^p\times L^q$ into Lebesgue and Lorentz spaces $L^{r,\alpha}.$ In several cases we identify the optimal Lorentz…

We consider different notions of capacity related to the parabolic $p$-Laplace equation. Our focus is on a variational notion, which is consistent in the full range $1<p<\infty$. For such a notion we show some basic properties as well as…

In this paper we study the regularity properties of the Gaussian Bessel potentials and Gaussian Bessel fractional derivatives on variable Gaussian Besov-Lipschitz spaces $B_{p(\cdot),q(\cdot)}^{\alpha}(\gamma_{d}),$ that were defined in a…

This paper deals with different characterizations of sets of nonlinear parabolic capacity zero, with respect to the parabolic p-Laplace equation. Specifically we prove that certain interior polar sets can be characterized by sets of zero…

Under different assumptions on the potential functions $b$ and $c$, we study the fractional equation $\left( I-\Delta \right)^{\alpha} u = \lambda b(x) |u|^{p-2}u+c(x)|u|^{q-2}u$ in $\mathbb{R}^N$. Our existence results are based on compact…

In this paper we will study the boundedness of Riesz Potentials, Bessel potentials and Fractional Derivatives on Gaussian Besov-Lipschitz spaces $B_{p,q}^{\alpha}(\gamma_d)$. Also these results can be extended to the case of Laguerre or…

Under the standard assumptions on the variable exponent $p(x)$ (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space $\mathfrak B^\alpha[L^{p(\cdot)}(\mathbb R^n)]$ in terms of the rate of…

We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional…

Considering potentials defined by Bessel kernel with Bessel convolution a Kerman-Sawyer type characterization of trace inequality is given. As an application an estimate on the least eigenvalue of Schr\"odinger-Bessel operators is derived.

We show that, for some Cantor sets in R^d, the capacity g_s associated to the s-dimensional Riesz kernel x/|x|^{s+1} is comparable to the capacity C_{2(d-s)/3,3/2} from non linear potential theory. It is an open problem to show that, when s…

We obtain convolution inequalities in Lebesgue and Lorentz spaces with power weights when the functions involved are assumed to be radially symmetric. We also present applications of these results to inequalities for Riesz potentials of…

In this article we study two classical potential-theoretic problems in convex geometry corresponding to a nonlinear capacity, $\mbox{Cap}_{\mathcal{A}}$, where $\mathcal{A}$-capacity is associated with a nonlinear elliptic PDE whose…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…

There are many interesting problems about the electrostatic potential of finitely many charges. We consider one of them concerning the intensity of the field, in other words, about the magnitude of the gradient of this potential. We want to…

In this paper we give an elementary proof that sets of zero $p,1$-Sobolev-Lorentz capacity are $\mathcal{H}^{n-p}$-null sets independently of non-linear potential theory. We further show that there exists a set of Sobolev-Lorentz-$(p,1)$…

We introduce a natural definition of $L^p$-convergence of maps, $p \ge 1$, in the case where the domain is a convergent sequence of measured metric space with respect to the measured Gromov-Hausdorff topology and the target is a…

We study a capacity theory based on a definition of Haj{\l} asz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower…

In this paper we define Bessel potentials in Ahlfors regular spaces using a Coifman type approximation of the identity, and show they improve regularity for Lipschitz, Besov and Sobolev-type functions. We prove density and embedding results…

This paper presents the nonlinear potential theory for mixed local and nonlocal $p$-Laplace type equations with coefficients and measure data, involving both superquadratic and subquadratic cases. We prove a class of universal pointwise…

We give a probabilistic characterisation of the Besov-Lipschitz spaces $Lip(\alpha,p,q)(X)$ on domains which support a Markovian kernel with appropriate exponential bounds. This extends former results of \cite{Jon,KPP1,KPP2,GHL} which were…