Related papers: On multiply monotone functions

Let $1<p,q<\infty ,\ \theta_1 \geq 0,\ \theta_2 \geq 0$ and let $a(x), b(x)$ be a weight functions. In the present paper we intend to study the function space $A_{q),\theta _{2}}^{p),\theta _{1}}\left( \mathbb R^n\right)$ consisting of all…

We consider the problem of testing equality of functions $f_j:[0,1]\to \mathbb{R}$ for $j=1,2,...,J$ the basis of $J$ independent samples from possibly different distributions under the assumption that the functions are monotone. We provide…

In the present paper, we give two new proofs for the necessary and sufficient condition $\alpha\le1$ such that the function $x^\alpha[\ln x-\psi(x)]$ is completely monotonic on $(0,\infty)$.

Let $f\colon \mathbb{R}_+\to\mathbb{R}$ be a continuous and strictly monotone function. In the main result of this paper, we show that, for a fixed $n\geq 2$, the $n$-variable mean $\mathscr{A}_f \colon \mathbb{R}_+^n \to \mathbb{R}_+$…

For $1<p\le 2$, we establish sharp inequalities for the Fourier transform of the characteristic function of the $l^p$-unit ball $B_p\subset\mathbb{R}^2$. We show that $$ \sup_{\boldsymbol{\omega} \in \mathbb{R}^2} \|\boldsymbol{\omega}…

We consider quasiradial Fourier multipliers, i.e. multipliers of the form $m(a(\xi))$ for a class of distance functions $a$. We give a necessary and sufficient condition for the multiplier transformations to be bounded on $L^p$ for a…

Let $A$ be an expansive dilation on $\mathbb{R}^n$, and $p(\cdot):\mathbb{R}^n\rightarrow(0,\,\infty)$ be a variable exponent function satisfying the globally log-H\"{o}lder continuous condition. Let $\mathcal{H}^{p(\cdot)}_A({\mathbb…

Let $a, b,c $ and $k$ be positive integers such that $1\leq a\leq b,a<c<2(a+b), c\ne b$ and $(a,b,c)=1$. Define the arithmetic function $f_k(a,b;c;n)$ by $$ \sum_{n=1}^{\infty}\frac{f_k(a,b;c;n)}{n^s}=\frac{\zeta (as)\zeta…

We prove the existence of gaps between all the different classes of matrix monotone functions defined on an interval, provided the interval is non trivial and different from the whole real line. We then show how matrix monotone functions…

We consider the bilinear Fourier multiplier operator with the multiplier written as a linear combination of a fixed bump function. For those operators we prove two transference theorems, one in amalgam spaces and the other in Wiener amalgam…

The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple…

This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.

The discrete Fourier transform of the greatest common divisor is a multiplicative function that generalises both the gcd-sum function and Euler's totient function. On the one hand it is the Dirichlet convolution of the identity with…

In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.

We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…

For a polynomial $f(X)=AX^d+C \in \mathbb{F}_p[X]$ with $A\neq 0$ and $d\geq 2$, we prove that if $d\;|\;p-1$ and $f^i(0)\neq f^j(0)$ for $0\leq i<j\leq N$, then $\#f^N(\mathbb{F}_p) \sim \frac{2p}{(d-1)N},$ where $f^N$ is the $N$-th…

We prove an explicit formula for the Fourier transform of $f(u(t))$, given the Fourier transform of $f(t)$, assuming $f\in L^2(-\infty,\infty)$ and $u$ sufficiently well behaved. We illustrate its usefulness by calculating the Fourier…

We study the subspaces of $L_p(\mathbb{R}^d)$ that consist of functions whose Fourier transforms vanish on a smooth surface of codimension $1$. We show that a subspace defined in such a manner coincides with the whole $L_p$ space for $p >…

The function f:X -> Y is called k-monotonically increasing if there is a partition X = X_1 U ... U X_k such that f|X_i : X_i -> Y is monotonically increasing for i=1,...,k. It is proved that a one-to-one function f:N -> N is k-monotonically…

We prove a structure theorem for multiplicative functions which states that an arbitrary bounded multiplicative function can be decomposed into two terms, one that is approximately periodic and another that has small Gowers uniformity norm…