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We determine multiplication and convolution topological algebras for classes of $\omega$-ultradifferentiable functions of Beurling type. Hypocontinuity and discontinuity of the multiplication and convolution mappings are also investigated.
The main purpose of this paper is to prove some density results of polynomials in Fock spaces of slice regular functions. The spaces can be of two different kinds since they are equipped with different inner products and contain different…
We present a new characterization of higher-order Sobolev spaces on the sphere. Building on the approach of Barcel\'o et al. (2020), we refine the square function they introduced for this purpose. In particular, we provide a detailed…
Using principles of the theory of smoothness spaces we give systematic constructions of scales of inverse-closed subalgebras of a given Banach algebra with the action of a d-parameter automorphism group. In particular we obtain the…
Apart from an account of classical preliminaries, this volume contains a systematic introduction to Sobolev spaces and functions of bounded variation with selected applications. This is installment III of a four part discussion of certain…
In this article we present Sobolev-type inequalities for the localization of pseudo-relativistic energy.
By proving an estimate of the sublevel sets for $(\omega,m)$-subharmonic functions we obtain a Sobolev type inequality that is then used to characterize the degenerate complex Hessian equations for such functions with bounded…
We study convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and obtain in this way new trace inequalities for deformed exponentials that may be considered as generalizations of…
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…
Motivated by a recent work of Schippa (2022), we consider local smoothing estimates for Schr\"{o}dinger equations in modulation spaces. By using the C\'{o}rdoba-Fefferman type reverse square function inequality and the bilinear Strichartz…
This paper establishes isomorphisms for the Laplace operator in weighted Sobolev spaces (WSS). These spaces are similar to standard Sobolev spaces, but they are endowed with weights prescribing functions growth or decay at infinity.…
To construct flexible nonlinear predictive distributions, the paper introduces a family of softplus function based regression models that convolve, stack, or combine both operations by convolving countably infinite stacked gamma…
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…
The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…
We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We…
The dynamics in the photosphere is governed by the multi-scale turbulent convection termed as granulation and supergranulation. It is important to derive 3-dimensional velocity vectors to understand the nature of the turbulent convection.…
We establish characterization of $H^1$ Sobolev spaces by certain square functions, improving previous results.
A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised…
We study translative integral formulas for certain translation invariant functionals on convex polytopes and discuss local extensions and applications to Poisson processes and Boolean models.
In these notes, we present versions of trace theorems for Sobolev spaces over an interval in the real line, and also a one-dimensional version of the well-known Poincare inequality.