相关论文: Optimal Sobolev embeddings for generalized Lorentz…

It is well known that Sobolev embeddings can be improved in the presence of symmetries. In this article, we considere the situation in which given a domain $\Omega=\Omega_1 \times \Omega_2$ in $\mathbb{R}^N$ with a cylindrical symmetry, and…

We propose a functional framework of fractional Sobolev spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak H\"ormander condition. We characterize these spaces as real interpolation of natural order intrinic…

Optimal weighted Sobolev-Lorentz embeddings with homogeneous weights in open convex cones are established, with the exact value of the optimal constant. These embeddings are non-compact, and this paper investigates the structure of their…

In this paper we propose a unified approach, based on limiting interpolation, to investigate the embeddings for the Sobolev space $(\dot{W}^k_p(\mathcal{X}))_0, \, \mathcal{X} \in \{\mathbb{R}^d, \mathbb{T}^d, \Omega\}$, in the subcritical…

It is well-known that the embedding of the Sobolev space of weakly differentiable functions into H\"{o}lder spaces holds if the integrability exponent is higher than the space dimension. In this paper, the embedding of the Sobolev functions…

We give an elementary proof of a compact embedding theorem in abstract Sobolev spaces. The result is first presented in a general context and later specialized to the case of degenerate Sobolev spaces defined with respect to nonnegative…

In this paper, we study symmetry-improved fractional Sobolev embeddings on closed Riemannian manifolds under the action of compact isometry groups. We prove that \(G\)-invariant fractional Sobolev spaces embed into higher \(L^p\) spaces,…

We study higher-order compact Sobolev embeddings on a domain $\Omega \subseteq \mathbb R^n$ endowed with a probability measure $\nu$ and satisfying certain isoperimetric inequality. Given $m\in \mathbb N$, we present a condition on a pair…

This paper introduces first order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally nonlinear class of generalised weakly differentiable functions and share key functional…

The continouity and compactness of embedding operators in in Sobolev-Lions type spaces are derived. By applying this result separability properties of degenerate anisotropic differential operator equations, well-posedeness and Strichartz…

We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the…

The paper is dedicated to the study of embeddings of the anisotropic Besov spaces $B^{\beta_1,...,beta_n}_{p;\theta_1,...,\theta_n}(\Bbb R^n)$ into Lorentz spaces. We find the sharp asymptotic behaviour of embedding constants when some of…

In this paper we present new embedding results for Musielak-Orlicz Sobolev spaces of double phase type. Based on the continuous embedding of $W^{1,\mathcal{H}}(\Omega)$ into $L^{\mathcal{H}_*}(\Omega)$, where $\mathcal{H}_*$ is the Sobolev…

This short note investigates the compact embedding of degenerate matrix weighted Sobolev spaces into weighted Lebesgue spaces. The Sobolev spaces explored are defined as the abstract completion of Lipschitz functions in a bounded domain…

We investigate asymptotically sharp upper and lower bounds for the approximation numbers of the compact Sobolev embeddings $\overset{\circ}{W}{^m}(\Omega)\hookrightarrow L_2(\Omega)$ and $ W^m(\Omega)\hookrightarrow L_2(\Omega)$, defined on…

We obtain symmetrization inequalities in the context of Fractional Hajlasz-Sobolev spaces in the setting of rearrangement invariant spaces and prove that for a large class of measures our symmetrization inequalities are equivalent to the…

Quantitative bounds for random embeddings of $\mathbb{R}^{k}$ into Lorentz sequence spaces are given, with improved dependence on $\varepsilon$.

In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Haj{\l}asz-Triebel-Lizorkin and Haj{\l}asz-Besov spaces in the general context…

We discuss the optimality of Cwikel-Solomyak estimates for the uniform operator norm and establish optimality of M.Z Solomyak's results \cite{Solomyak1995} within the class of Orlicz spaces. Our methods are based on finding the optimal…

We study compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces with variable exponents on both bounded and unbounded metric measure spaces. We establish sufficient conditions for compactness, and under additional assumptions, we…