Related papers: Bessel Potential Spaces and Complex Interpolation:…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
We show that a domain is an extension domain for a Haj\l asz-Besov or for a Haj\l asz-Triebel-Lizorkin space if and only if it satisfies a measure density condition. We use a modification of the Whitney extension where integral averages are…
In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of…
This paper investigates functional inequalities involving Besov spaces and functions of bounded variation, when the underlying metric measure space displays different local and global structures. Particular focus is put on the $L^1$ theory…
A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…
In this work, we introduce the Kaiser-Bessel interpolation basis for the particle-mesh interpolation in the fast Ewald method. A reliable a priori error estimate is developed to measure the accuracy of the force computation in correlated…
The paper is devoted to Mellin convolution operators with meromorphic kernels in Bessel potential spaces. We encounter such operators while investigating boundary value problems for elliptic equations in planar 2D domains with angular…
Our main purpose is to establish Gagliardo-Nirenberg type inequalities using fractional homogeneous Sobolev spaces, and homogeneous Besov spaces. In particular, we extend some of the results obtained by the authors in [1, 2, 3, 7, 16, 21].
Interpolation inequalities play an important role in the study of PDEs and their applications. There are still some interesting open questions and problems that related to integral estimates and regularity of solutions to the elliptic…
In this paper, we introduce a class of homeomorphisms between metric spaces, which are locally biH\"{o}lder continuous mappings. Then an embedding result between Besov spaces induced by locally biH\"{o}lder continuous mappings between…
New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…
We define distributions on an abstract measure space endowed with a sequence of partitions, and introduce analogues of Besov spaces with negative smoothness in this setting. In particular, we describe these spaces of distributions using…
We explicitly describe all Hilbert function spaces that are interpolation spaces with respect to a given couple of Sobolev inner product spaces considered over $\mathbb{R}^{n}$ or a half-space in $\mathbb{R}^{n}$ or a bounded Euclidean…
We consider fractional Sobolev spaces $H^\theta$, $\theta\in (0,1)$, on 2D domains and $H^1$-conforming discretizations by globally continuous piecewise polynomials on a mesh consisting of shape-regular triangles and quadrilaterals. We…
In this paper we investigate the asymptotic behaviour of Weyl numbers of embeddings of tensor product Besov spaces into Lebesgue spaces. These results will be compared with the known behaviour of entropy numbers.
We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fractals.
This paper describes the partial wave expansion and integral representation of Bessel beams in free space and in the presence of dispersion. The expansion of the Bessel beam wavepacket with constant spectrum is obtained as well.…
In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with H\"{o}lder continuous coefficients. This is of course out of reach by using…
To analyze the absolute condition number of multivariate polynomial interpolation on Lissajous-Chebyshev node points, we derive upper and lower bounds for the respective Lebesgue constant. The proof is based on a relation between the…
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…