Related papers: A note on characterization of $H^1$ Sobolev spaces…

For $1/2<p<1$, a description of inner functions whose derivative is in the Hardy space $H^p$ is given in terms of either their mapping properties or the geometric distribution of their zeros.

A new representation is proposed for functions in a Sobolev space with dominating mixed smoothness on an $N$-dimensional hyperrectangle. In particular, it is shown that these functions can be expressed in terms of their highest-order mixed…

We study nonuniform Sobolev spaces, i.e., spaces of functions whose partial derivatives lie in possibly different Lebesgue spaces. Although standard proofs do not apply, we show that nonuniform Sobolev spaces share similar properties as the…

This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial approximations for functions in these…

We obtain sharp embeddings from the Sobolev space $W^{k,2}_0(-1,1)$ into the space $L^1(-1,1)$ and determine the extremal functions. This improves on a previous estimate of the sharp constants of these embeddings due to Kalyabin.

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

In the setting of the Euclidean space equipped with an arbitrary Radon measure, we prove the equivalence between several notions of function of bounded variation present in the literature. We also study the relation between various…

We describe a recent, one-parameter family of characterizations of Sobolev and BV functions on $\mathbb{R}^n$, using sizes of superlevel sets of suitable difference quotients. This provides an alternative point of view to the BBM formula by…

We give a characterization of metric space valued Sobolev maps in terms of weak* derivatives. This corrects a previous result by Haj{\l}asz and Tyson.

We characterize the boundedness of square functions in the upper half-space with general measures. The short proof is based on an averaging identity over good Whitney regions.

We develop characterizations for Sobolev spaces of potential type on graded Lie groups, by means of Littlewood-Paley square functions, and Strichartz functionals involving second-order differences. A key role is played by some mean value…

We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvment of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin type estimates of…

In this paper, we show that any Sobolev norm of nonnegative integer order of radially symmetric functions is equivalent to a weighted Sobolev norm of their radial profile. This establishes in terms of weighted Sobolev spaces on an interval…

We provide a new characterization of the logarithmic Sobolev inequality.

We establish point wise inequalities for Sobolev functions on a wider class of outward cuspidal domains. It is a generalization of an earlier result by the author and his collaborators

In this paper we present a new characterization of the Sobolev space $W^{1,p}$, $1<p<\infty$ which is a higher dimensional version of a result of Waterman. We also provide a new and simplified proof of a recent result of Alabern, Mateu and…

We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of the Euclidean space and the relation between these spaces and traces of classical Sobolev spaces.

In this work we consider refined geometric characterizations of mappings generate composition operators on Sobolev spaces. The detailed proofs in the cases $n-1<q<n$ and $n>q$ are given.

The Hodge decomposition is well-known for compact manifolds. The result has been extended by Kodaira to include non-compact manifolds and $L^2$ forms. We further extend the Hodge decomposition to the Sobolev space $H^1$ for general…

Using tools from the theory of operator ideals and s-numbers, we develop a general approach to transfer estimates for $L_2$ -approximation of Sobolev functions into estimates for $L_\infty$-approximation, with precise control of all…