In this paper, we determine the $L^p(\mathbb{R})\times L^q(\mathbb{R})\rightarrow L^r(\mathbb{R})$ boundedness of bilinear Hilbert transform $H_{\gamma}(f,g)$ along a convex curve $\gamma$ $$H_{\gamma}(f,g)(x):=\mathrm{p.\,v.}\int_{-\infty}^{\infty}f(x-t)g(x-\gamma(t)) \,\frac{\textrm{d}t}{t},$$ where $p$, $q$, and $r$ satisfy $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$, $r>\frac{1}{2}$, $p>1$, $q>1$...

The aim of the paper is to prove following result concerning moduli curve families in Heisenberg group. Let $\Omega$ be a domain group foliated by family $\Gamma$ legendrian curves. Assume that there quadratic differential $q$ on kernel an operator defined \cite{Tim2} and every horizontal trajectory for $q$. $l_\Gamma : \Omega \rightarrow ]0,+\infty[$ function associates point $p\in \Omega$, $q...

In this paper, the complete monotonicity property of functions involving the q -gamma function is proven and used to establish sharp inequalities for the q -gamma and the q -polygamma functions for all q > 0 . These bounds for the q -gamma and the q -polygamma functions refine those given by Salem [17]. Mathematics subject classification (2010): 33D05, 26D07, 26A48.

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

We investigate conditions for logarithmic complete monotonicity of product ratios gamma and q-gamma functions whose arguments are linear the variable. give necessary sufficient in terms nonnegativity a certain explicitly written measure q case elementary function classical $$q=1$$ case. In latter we further provide simple new leading to many examples logarithmically completely monotonic ratios....

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

begin{abstract} the relations between the spectrum of the matrix $q+r$ and the spectra of the matrices $(gamma + delta)q+(alpha + beta)r-qr-rq$, $qr-rq$, $alpha beta r-qrq$, $alpha rqr-(qr)^{2}$, and $beta r-qr$ have been given on condition that the matrix $q+r$ is diagonalizable, where $q$, $r$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $...