Related papers: Inequalities with angular integrability and applic…

We obtain sharp weighted estimates for solutions of the equation $\partial$ u = f in a lineally convex domain of finite type. Precisely we obtain estimates in the spaces L p ($\Omega$,$\delta$ $\gamma$), $\delta$ being the distance to the…

Some integration techniques for real-valued functions with respect to vector measures with values in Banach spaces (and viceversa) are investigated in order to establish abstract versions of classical theorems of Probability and Stochastic…

We extend the range of parameters associated with the Gagliardo-Nirenberg interpolation inequalities in the fractional Coulomb-Sobolev spaces for radial functions. We also study the optimality of this newly extended range of parameters.

We study weak-type estimates and exponential integrability for the variable order Riesz potential. As an application we prove an exponential integrability result with respect to the Hausdorff content for functions from variable exponent…

We prove sharp local smoothing estimates for wave equations on compact Riemannian manifolds in $n+1$ dimensions for odd $n$ and obtain improved estimates in even dimensions. This is achieved by deriving local smoothing estimates for certain…

A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequality. New results are obtained for diagonal trace…

We study nonlinear elliptic equations that arise as stationary states of inhomogeneous nonlinear Schr\"odinger equations with competing singular nonlinearities. The model involves the Laplacian combined with weighted power-type terms and…

In this note, we prove a new uncertainty principle for functions with radial symmetry by differentiating a radial version of the Stein-Weiss inequality. The difficulty is to prove the differentiability in the limit of the best constant…

We prove compactness of the embeddings in Sobolev spaces for fractional super and sub harmonic functions with radial symmetry. The main tool is a pointwise decay for radially symmetric functions belonging to a function space defined by…

We prove a higher regularity result for weak solutions to nonlinear nonlocal equations along the integrability scale of Bessel potential spaces $H^{s,p}$ under a mild continuity assumption on the kernel. By embedding, this also yields…

This paper establishes global weighted Calder\'on-Zygmund type regularity estimates for weak solutions of a class of generalized Stokes systems in divergence form. The focus of the paper is on the case that the coefficients in the…

We prove certain weighted Strichartz estimates and use these to prove a sharp theorem for global existence of small amplitude solutions of $\square u= |u|^p$, thus verifying the so-called "Strauss conjecture".

In this paper we give a thorough study of Lipschitz spaces. We obtain the following new results: (1) Sharp Jawerth-Franke-type embeddings between the Besov and Lipschitz spaces extending the classical results for Besov and Sobolev spaces;…

We prove that the geodesic equations of all Sobolev metrics of fractional order one and higher on spaces of diffeomorphisms and, more generally, immersions are locally well posed. This result builds on the recently established real analytic…

This paper deals with the fractional Sobolev spaces $W^{s, p}(\Omega)$, with $s\in (0, 1]$ and $p\in[1,+\infty]$. Here, we use the interpolation results in [4] to provide suitable conditions on the exponents $s$ and $p$ so that the spaces…

We investigate weighted Lebesgue space estimates for the Bergman projection on a simply connected planar domain via the domain's Riemann map. We extend the bounds which follow from a standard change-of-variable argument in two ways. First,…

In this paper, we study different types of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. The function spaces can be defined by means of the Littlewood-Paley theory in the field of Fourier analysis, while there are…

In this paper we study special bases of certain spaces of half-integral weight weakly holomorphic modular forms. We establish a criterion for the integrality of Fourier coefficients of such bases. By using recursive relations between Hecke…

We study a filtered Lie splitting scheme for the cubic nonlinear Schr\"{o}dinger equation. We establish error estimates at low regularity by using discrete Bourgain spaces. This allows us to handle data in $H^s$ with $0<s<1$ overcoming the…

We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class $A_\infty$. The main tool is a discretization in terms of an almost orthogonal wavelet expansion…