Related papers: Generalized $\alpha$-variation and Lebesgue equiva…

We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz…

A second-order generalization of the fundamental Lepage form of geometric calculus of variations over fibered manifolds with 2-dimensional base is described by means of insisting on (i) equivalence relation "Lepage differential 2-form is…

We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^{\Omega}_{p,\theta}(\mathbb{R}^d)$ by sums of de la Vallee Poussin type in the metrics space…

For real symmetric positive definite matrices $A$ and $B$, we characterize when a function $f \in L^2(\mathbb{R}^d)$ satisfies \[ |f(x)| \lesssim e^{-(\frac12 - \lambda) \langle Ax, x\rangle} \quad \text{and} \quad |\widehat{f}(\xi)|…

The purpose of this paper is to investigate the following invariance equation involving two $2$-variable generalized Bajraktarevi\'c means, i.e., we aim to solve the functional equation $$…

We study the problem estimation of classical Lebesgue-Riesz and Grand Lebesgue Norm for the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces as well as from the modified Besov's spaces.

A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th…

Let $f, g: \mathbb{R}^2 \to \mathbb{R}$ be two submersion functions and $\mathscr{F}(f)$ and $\mathscr{F}(g)$ be the regular foliations of $\mathbb{R}^2$ whose leaves are the connected components of the levels sets of $f$ and $g$,…

For functions from the set of generalized Poisson integrals $C^{\alpha,r}_{\beta}L_{p}$, $1\leq p <\infty$, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the…

We show that there exists an integrable function on the $n$-sphere $(n\ge 2)$, whose Ces\`aro (C,$\frac{n-1}{2}$) means with respect to the spherical harmonic expansion diverge unboundedly almost everywhere. By studying equivalence…

A Sobolev type embedding for radially symmetric functions on the unit ball $B$ in $\mathbb R^n$, $n\geq 3$, into the variable exponent Lebesgue space $L_{2^\star + |x|^\alpha} (B)$, $2^\star = 2n/(n-2)$, $\alpha>0$, is known due to J.M. do…

Let $f$ be a normalized holomorphic cusp form for $SL_2(\mathbb{Z})$ of weight $k$ with $k\equiv0\bmod 4$. By the Kuznetsov trace formula for $GL_3(\mathbb R)$, we obtain the first moment of central values of $L(s,f\otimes \phi)$, where…

Let $g$ be a finite dimensional real Lie algebra. Let $r:g\to End(V)$ be a representation of $g$ in a finite dimensional real vector space. Let $C_{V}=(End(V)\tens S(g))^{g}$ be the algebra of $End(V)$-valued invariant differential…

Lepage equivalents of Lagrangians are a higher order, field-theoretical generalization of the notion of Poincare-Cartan form from mechanics and play a similar role: they give rise to a geometric formulation (and to a geometric…

We address the question of non-vanishing of $L(1,f)$ where $f$ is an algebraic-valued, periodic arithmetical function. We do this by characterizing algebraic-valued, periodic functions $f$ for which $L(1,f)=0$. The case of odd functions was…

We determine a four-function generalization of the Plebanski spacetime, depending on three arbitrary functions of the radial coordinate, and one function on the angular coordinate. For the generalized Plebanski spacetime, we analyze the…

In 2014, Michal Lewicki and Andrzej Olbry\'s proved that if a real valued function $f$ defined on the real line satisfies the conditional functional equation \[ f(tx + (1-t)y) = t f(x) + (1-t) f(y),\qquad x\leq y, \] called…

In this article, we look for the weight functions (say $g$) that admits the following generalized Hardy-Rellich type inequality: $ \int_{\Omega} g(x) u^2 dx \leq C \int_{\Omega} |\Delta u|^2 dx, \forall u \in \mathcal{D}^{2,2}_0(\Omega), $…

In this paper, we investigate and find a necessary and sufficient condition for a function to be absolutely continuous over $\mathbb{R}$ (denoted by $AC(\mathbb{R})$) or any unbounded interval in $\mathbb{R}$ . Note that the Lebesgue's…

The main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on $^*$-algebras. We describe the extreme points of order intervals, and give a nontrivial sufficient…