相关论文: Strong A-infinity weights, Besov and Sobolev capac…

Given a homeomorphism $f\colon X\to Y$ between $Q$-dimensional spaces $X,Y$, we show that $f$ satisfying the metric definition of quasiconformality outside suitable exceptional sets implies that $f$ belongs to the Sobolev class…

This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights $w:=\exp(-Q)$ with finite moments and with smooth external fields $Q:\mathbb R\to [0,\infty)$, with varying…

We prove that weakly differentiable weights $w$ which, together with their reciprocals, satisfy certain local integrability conditions, admit a unique associated first-order $p$-Sobolev space, that is \[H^{1,p}(\mathbb{R}^d,w\,\d…

Consider a H\"older continuous potential $\phi$ defined on the full shift $A^\nn$, where $A$ is a finite alphabet. Let $X\subset A^\nn$ be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$…

We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on $\R^d$, equipped with power weights $w(x) = |x|^\gamma$, $\gamma>-d$. We prove two-weight Sobolev embeddings for these spaces. Moreover, we…

We consider the weak-type inequality for Littlewood-Paley square functions on A_p weighted Lebesgue spaces. Of interest is the sharp in the A_p characteristic estimate. The case of 1<p<2 is subcritical, and the sharp power of 1/p is…

In this article, with introducing concepts of variable scalar $\mathcal{A}_{p(\cdot),\infty}$ weights and variable matrix $\mathscr{A}_{p(\cdot),\infty}$ weights, we seek a comprehensive theory of $A_\infty$ weights within the framework of…

Serre obtained the p-adic limit of the integral Fourier coefficient of modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on…

Let $(\operatorname{X},\operatorname{d},\mu)$ be a metric measure space with uniformly locally doubling measure $\mu$. Given $p \in (1,\infty)$, assume that $(\operatorname{X},\operatorname{d},\mu)$ supports a weak local $(1,p)$-Poincar\'e…

In this article, for $N \geq 2, s \in (1,2), p\in (1, \frac{N}{s}), \sigma=s-1 $ and $a \in [0, \frac{N-sp}{2})$, we establish an isometric isomorphism between the higher order fractional weighted Beppo-Levi space \begin{align*} {\mathcal…

We prove non-uniqueness of weak solutions to the forced $\alpha$-SQG equation with Sobolev regularity $W^{s,p}$ in the supercritical regime $s < \alpha + \frac{2}{p}$, covering the 2D Euler equation ($\alpha = 0$), the Surface…

We show that if a measure of dimension $s$ on $\mathbb{R}^d$ admits $(p,q)$ Fourier restriction for some endpoint exponents allowed by its dimension, namely $q=\tfrac{s}{d}p'$ for some $p>1$, then it is either absolutely continuous or…

We study connections between the problem of the existence of positive solutions for certain nonlinear equations and weighted norm inequalities. In particular, we obtain explicit criteria for the solvability of the Dirichlet problem…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove a new Cartan-type property for the fine topology in the case $p=1$. Then we use this property to prove the existence of…

The paper is devoted to two-weight estimates for the fractional maximal operators $\mathcal{M}^\alpha$ on general probability spaces equipped with a tree-like structure. For given $1<p\leq q<\infty$, we study the sharp universal upper bound…

Let $0<\alpha<1$ and $\frac{1}{q}=1-\alpha$. We first obtain that the function $\omega :\mathbb{Z} \rightarrow (0,\infty)$ belongs to weight class of $\mathcal{A} (1,q)(\mathbb{Z})$ if and only if discrete fractional maximal operator…

We investigate properties of measures in infinite dimensional spaces in terms of Poincar\'e inequalities. A Poincar\'e inequality states that the $L^2$ variance of an admissible function is controlled by the homogeneous $H^1$ norm. In the…

We study the quantum affine superalgebra $U_q(Lsl(M,N))$ and its finite-dimensional representations. We prove a triangular decomposition and establish a system of Poincar\'{e}-Birkhoff-Witt generators for this superalgebra, both in terms of…

The main subject of this paper is equilibrium problems on an unbounded conductor $\Sigma$ of the complex plane in the presence of a weakly admissible external field. An admissible external field $Q$ on $\Sigma$ satisfies, along with other…

Although numerous studies have focused on normal Besov spaces, limited studies have been conducted on exponentially weighted Besov spaces. Therefore, we define exponentially weighted Besov space $VB_{p,q}^{\delta,w}(\mathbb{R}^d)$ whose…