Related papers: Outer functions in analytic weighted Lipschitz alg…

We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…

We characterize all logarithmic, holomorphic vector-valued modular forms which can be analytically continued to a region strictly larger than the upper half-plane.

The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.

We calculate certain ext-groups between modules for a linear algebraic group. The results are in agreement with the Lusztig conjecture.

In this work we extend the concept of the Lipschitz saturation of an ideal defined in [5] to the context of modules in some different ways, and we prove they are generically equivalent.

To minimize or upper-bound the value of a function "robustly", we might instead minimize or upper-bound the "epsilon-robust regularization", defined as the map from a point to the maximum value of the function within an epsilon-radius. This…

We focus on the outer length billiard dynamics, acting on the exterior of a strictly-convex planar domain. We first show that ellipses are totally integrable. We then provide an explicit representation of first order terms for the formal…

For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…

We present a complete classification of complex plane algebraic curves, equipped with the induced Euclidean, up to global bilipschitz homeomorphism.

Let $A$ be a finite-dimensional, commutative algebra over $\mathbb{R}$ or $\mathbb{C}$. The notion of $A$-differentiable functions on $A$ is extended to the notion of $A$-differentiable functions on a finitely generated $A$-module $B$. Let…

We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…

All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.

We study Lipschitz continuity for solutions of the $\bar{\alpha}$-Poisson equation in planar cases. We also review some recently obtained results. As corolary we can restate results for harmonic and gradient harmonic functions.

Some notes and observations on analytic functions defined on an annulus

We give the sharp conditions for boundedness of Hausdorff operators on certain modulation and Wiener amalgam spaces.

We prove a new general multiplicity estimate applicable to sets of functions without any assumption on algebraic independence. The multiplicity estimates are commonly used in determining measures of algebraic independence of values of…

In this note we show that gradient of Harmonic functions on a smooth domain with Lipschitz boundary values is pointwise bounded by a universal function which is in $L^p$ for all finite $p\geq 1$.

We present some foundational results about the outer length billiard system, including its generating function and the invariant area form. We describe the limiting behavior of the orbits far away from the billiard table: the orbits of the…

Locally affine Lie algebras are generalizations of affine Kac--Moody algebras with Cartan subalgebras of infinite rank whose root system is locally affine. In this note we study a class of representations of locally affine algebras…

Newtonian spaces generalize first-order Sobolev spaces to abstract metric measure spaces. In this paper, we study regularity of Newtonian functions based on quasi-Banach function lattices. Their (weak) quasi-continuity is established,…