Related papers: Interpolation inequalities in function spaces of S…

We consider a homogeneous fractional Sobolev space obtained by completion of the space of smooth test functions, with respect to a Sobolev--Slobodecki\u{\i} norm. We compare it to the fractional Sobolev space obtained by the $K-$method in…

In this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the…

By employing harmonic analysis techniques, we derive weak-type Caffarelli-Kohn-Nirenberg inequalities under natural parameter conditions. A key feature of these weak-type versions is that they remain valid even at critical parameter values…

We obtain sharp Hardy inequalities on antisymmetric functions where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the previously published paper \cite{HL}, where Hardy's inequalities were…

Embeddings among fractional Orlicz-Sobolev spaces with different smoothness are characterized. The equivalence of their Gagliardo-Slobodeckij norms to norms defined via Littlewood-Paley decompostions, via oscillations, or via Besov type…

We revisit entropy methods to prove new sharp trace logarithmic Sobolev and sharp Gagliardo-Nirenberg-Sobolev inequalities on the half space, with a focus on the entropy inequality itself and not the actual flow, allowing for somewhat…

The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in…

We obtain estimates in Besov, Lizorkin-Triebel and Lorentz spaces of differential forms on R^n in terms of their L^1 norm.

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…

We study traces of weighted Triebel-Lizorkin spaces $F^s_{p,q}({\mathbb R}^n,w)$ on hyperplanes ${\mathbb R}^{n-k}$, where the weight is of Muckenhoupt type. We concentrate on the example weight $w_\alpha(x) = |x_n|^\alpha$ when $|x_n|\leq…

We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.

In this short article we generalize the Sobolev's inequalities for the module of continuity for the functions belonging to the classical Lebesgue space on the (Bilateral) Grand Lebesgue spaces. We construct also some examples in order to…

We prove several Sobolev inequalities, which are then used to establish a fractional Hardy-Sobolev- Maz'ya inequality on the upper halfspace.

This is a continuation of our previous work 0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity…

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…

We study fractional variants of the quasi-norms introduced by Brezis, Van Schaftingen, and Yung in the study of the Sobolev space $\dot W^{1,p}$. The resulting spaces are identified as a special class of real interpolation spaces of…

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,…

This book provides a gentle introduction to fractional Sobolev spaces, which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of…

In a previous paper we developed a new method to obtain symmetrization inequalities of Sobolev type for functions in $W_{0}^{1,1}(\Omega)$. In this paper we extend our method to Sobolev functions that do not vanish at the boundary.

Linear interpolation inequalities that combine Hardy's inequality with sharp Sobolev embedding are obtained using classical arguments of Hardy and Littlewood (Bliss lemma). Such results are equivalent to Caffarelli-Kohn-Nirenberg…