Related papers: Limits at infinity for functions in fractional Sob…

We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary

We study the convergence and divergence of the wavelet expansion of a function in a Sobolev or a Besov space from a multifractal point of view. In particular, we give an upper bound for the Hausdorff and for the packing dimension of the set…

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

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded…

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…

We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…

We develop a new method suitable for establishing lower bounds on the ball measure of noncompactness of operators acting between considerably general quasinormed function spaces. This new method removes some of the restrictions…

We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on…

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best…

Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, research on fractional problems remains limited, with most of…

We introduce the notion of kinetic maximal $L^2$-regularity with temporal weights for the (fractional) Kolmogorov equation. In particular, we determine the function spaces for the inhomogeneity and the initial value which characterize the…

After proving the equivalence of the Bessel $K$-functional and the corresponding spherical modulus of smoothness we define fractional Bessel-Sobolev spaces. As an analog of the classical one the imbedding relation of fractional…

We consider the equivalence of some norms in Sobolev spaces on bounded domains of the d-dimensional real Euclidean space and also in Sobolev spaces on the boundaries of those domains.

We introduce Herz-Sobolev spaces, which unify and generalize the classical Sobolev spaces. We will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Sobolev spaces.…

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…

We deduce an extension theorem for the so-called Sobolev-Grand Lebesgue Spaces defined on the suitable subsets of the whole finite-dimensional Euclidean space, and estimate the norms of correspondent extension operator, which may be choosed…

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.

In this paper, we study the existence of extremal functions of the discrete Sobolev inequality and Hardy-Littlewood-Sobolev inequality on lattice graphs. We introduce the discrete Concentration-Compactness principle, and prove the existence…

We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.