Related papers: Fractional Sobolev spaces with power weights

It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with…

In this paper we investigate the boundedness of sublinear operators generated by fractional integrals as well as sublinear operators generated by Calder\`on-Zygmund operators on generalized weighted Morrey spaces and generalized weighted…

Let $G$ be an Orlicz function and let $ \alpha, \beta, s$ be positive real numbers. Under certain conditions on the Orlicz function $ G $, we establish some continuous embeddings results between the fractional order Orlicz-Sobolev spaces…

We characterize the fractional Sobolev inequality with fractional isocapacitary and isoperimetric inequalities. We give a sufficient condition and examples so that the fractional capacity of the closure of an open set is bounded above by…

We prove that for any topological space $X$ of countable tightness, each \sigma-convex subspace $\F$ of the space $SC_p(X)$ of scatteredly continuous real-valued functions on $X$ has network weight $nw(\F)\le nw(X)$. This implies that for a…

In our previous publication [{\em Calc. Var. Partial Differential Equations}, 60(1):Paper No. 16, 27, 2021], we delved into examining a critical Sobolev-type embedding of a Sobolev weighted space into an exponential weighted Orlicz space.…

We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the time and one spatial variable except one coefficient, which…

We study the distance in the Zygmund class $\Lambda_{\ast}$ to the subspace $\operatorname{I}(\operatorname{BMO})$ of functions with distributional derivative with bounded mean oscillation. In particular, we describe the closure of…

We describe the $(p,q)$ Fock--Carleson measures for weighted Fock--Sobolev spaces in terms of the objects $(s,t)$-Berezin transforms, averaging functions, and averaging sequences on the complex space $\mathbb{C}^n$. The main results show…

We introduce a new family of function spaces, the fractional generalized Sobolev-Orlicz spaces $\Lambda^{s,A}_0(\Omega)$, where $A$ is a generalized $\Phi$-function satisfying the $(\mathrm{Inc})_{p}$ and $(\mathrm{Dec})_{q}$ conditions for…

We continue the study of the space $BV^\alpha(\mathbb R^n)$ of functions with bounded fractional variation in $\mathbb R^n$ and of the distributional fractional Sobolev space $S^{\alpha,p}(\mathbb R^n)$, with $p\in [1,+\infty]$ and…

We study Poincare-Sobolev type inequalities for compactly supported smooth functions which are defined in the Euclidean $n$-space and whose absolute value of gradient are Choquet $\delta /n$-integrable with respect to the…

Assuming that $S$ is the space of functions of regular variation, $\omega\in S$, $0< p<\infty$, a function $f$ holomorphic in $B^n$ is said to be of Besov space $B_p(\omega)$ if $$\|f\|^p_{B_p(\omega )}=\int_{B^n}…

We show that if $u$ is a compactly supported distribution on the complex plane such that, for every pair of entire functions $f,g$, \[ \langle u,f\overline{g}\rangle=\langle u,f\rangle\langle u,\overline{g}\rangle, \] then $u$ is supported…

We introduce and study a family of spaces of entire functions in one variable that generalise the classical Paley-Wiener and Bernstein spaces. Namely, we consider entire functions of exponential type $a$ whose restriction to the real line…

We consider the problem of finding the optimal exponent in the Moser-Trudinger inequality \[ \sup \left\{\int_\Omega \exp{\left(\alpha\,|u|^{\frac{N}{N-s}}\right)}\,\bigg|\,u \in…

We consider here Musielak-Orlicz Sobolev (MOS) spaces $W^{k,\Phi}(\Omega)$, where $\Omega$ is an open subset of $\mathbb{R}^d$, $k\in\mathbb{N}$ and $\Phi$ is a Musielak-Orlicz function. The main outcomes consist of the results on density…

Let $\gamma\in\mathbb{R}\setminus\{0\}$ and $X(\mathbb{R}^n)$ be a ball Banach function space satisfying some extra mild assumptions. Assume that $\Omega=\mathbb{R}^n$ or $\Omega\subset\mathbb{R}^n$ is an $(\varepsilon,\infty)$-domain for…

Let $\Omega$ be a product domain in $\mathbb C^n, n\ge 2$, where each slice has smooth boundary. We observe that the canonical solution operator for the $\bar\partial$ equation on $\Omega$ is bounded in $W^{k,p}(\Omega)$, $k\in \mathbb Z^+,…

Let $T$ be a non-degenerate Calder\'on-Zygmund operator and let $b:\mathbb{R}^d\to\mathbb{C}$ be locally integrable. Let $1<p\leq q<\infty$ and let $\mu^p\in A_p$ and $\lambda^q\in A_q,$ where $A_{p}$ denotes the usual class of Muckenhoupt…