Related papers: Hardy inequalities in Triebel-Lizorkin spaces II. …

We prove an inequality of Hardy type for functions in Triebel-Lizorkin spaces. The distance involved is being measured to a given Ahlfors d-regular set in R^n, with n-1<d<n. As an application of the Hardy inequality, we consider boundedness…

This paper provides equivalence characterizations of homogeneous Triebel-Lizorkin and Besov-Lipschitz spaces, denoted by $\dot{F}^s_{p,q}(\mathbb{R}^n)$ and $\dot{B}^s_{p,q}(\mathbb{R}^n)$ respectively, in terms of maximal functions of the…

We present a new notion, the upper Aikawa codimension, and establish its equivalence with the upper Assouad codimension in a metric space with a doubling measure. To achieve this result, we first prove variant of a local fractional Hardy…

We find sharp constants in fractional Hardy inequalities for weighted Triebel--Lizorkin seminorms on the whole space and half-spaces. Our results generalize recently obtained weighted fractional Hardy inequalities for Gagliardo seminorms,…

In this paper, we will introduce and study several types of Kakeya inequalities by the maximal functions in Hardy spaces in $\RR^n$,\,$(n\geq2)$, and we could obtain several inequalities associated with the Kakeya inequalities. We will show…

This note contains two simple observations. First, by the weak factorization of product $H^1$ (Ferguson--Lacey, Lacey--Terwilleger), we obtain a multi-parameter analogue of Hardy's inequality. Second, as a dual statement, the Fourier…

Let $\alpha\in\mathbb R$, $q\in(0,\infty]$, $p\in(0,\infty)$, and $W$ be an $A_p(\mathbb{R}^n,\mathbb{C}^m)$-matrix weight. In this article, the authors characterize the matrix-weighted Triebel-Lizorkin space $\dot{F}_{p}^{\alpha,q}(W)$ via…

In this paper, we identify the duals of Triebel-Lizorkin spaces of generalized smoothness. In some particular cases these function spaces are just weighted Triebel-Lizorkin spaces. To do these, we will be working at the level of sequence…

In this article we prove both norm and modular Hardy inequalities for a class functions in one-dimensional fractional Orlicz-Sobolev spaces.

In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space $F^s_{p,q}(\Omega)$ in terms of first-order differences in a uniform domain $\Omega$. The characterization is valid for any positive, non-integer real…

We establish fractional Hardy-type inequalities in a bounded domain with plump complement. In particular our results apply in bounded C^\infty domains and Lipschitz domains.

In this work we give some maximal inequalities in Triebel-Lizorkin spaces, which are "$\dot{F}_{\infty}^{s,q}$-variants" of Fefferman-Stein vector-valued maximal inequality and Peetre's maximal inequality. We will give some applications of…

As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent open question by Musina and Nazarov. In the proof we apply a new version of the…

The aim of this paper is to prove duality of Triebel-Lizorkin spaces $% F_{1,q\left( \cdot \right) }^{\alpha \left( \cdot \right) }$. First, we prove the duality of associated sequence spaces. Then from the so-called $% \varphi $-transform…

We prove a Hardy-Sobolev-Maz'ya inequality for arbitrary domains \Omega\subset\R^N with a constant depending only on the dimension N\geq 3. In particular, for convex domains this settles a conjecture by Filippas, Maz'ya and Tertikas. As an…

We provide a family of global weighted Sobolev inequalities and Hardy inequalities on PI spaces with possibly non-maximal volume growth. Our results apply notably to non-trivial Ahlfors regular spaces like Laakso spaces and Kleiner-Schioppa…

We consider Littlewood-Paley functions associated with non-isotropic dilations. We prove that they can be used to characterize the parabolic Hardy spaces of Calder\'{o}n-Torchinsky.

Interpolation inequalities in Triebel-Lizorkin-Lorentz spaces and Besov-Lorentz spaces are studied for both inhomogeneous and homogeneous cases. First we establish interpolation inequalities under quite general assumptions on the parameters…

In this paper, by using the atomic decomposition theorem for weighted weak Hardy spaces, we will show the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and…

We prove that in variable exponent spaces $L^{p(\cdot)}(\Omega)$, where $p(\cdot)$ satisfies the log-condition and $\Omega$ is a bounded domain in $\mathbf R^n$ with the property that $\mathbf R^n \backslash \bar{\Omega}$ has the cone…