Related papers: Singular maximal functions and Radon transforms ne…

We consider $L$-functions $L_1,\ldots,L_k$ from the Selberg class which have polynomial Euler product and satisfy Selberg's orthonormality condition. We show that on every vertical line $s=\sigma+it$ with $\sigma\in(1/2,1)$, these…

Let G/H be a hyperbolic space over R C or H, and let K be a maximal compact subgroup of G. Let D denote a certain explicit invariant differential operator, such that the non-cuspidal discrete series belong to the kernel of D. For any…

In the paper we consider Calder\'{o}n-Zygmund operators in nonhomogeneous spaces. We are going to prove the analogs of classical results for homogeneous spaces. Namely, we prove that a Calder\'{o}n-Zygmund operator is of weak type if it is…

The standard Radon transform of holomorphic functions is not always well defined, as the integration of such functions over planes may not converge. In this paper, we introduce new Radon-type transforms of co-(real)dimension $2$ for…

In this paper it is shown that for $\Omega\in L\log L(\mathbb{S}^{d-1})$, the rough maximal singular integral operator $T_\Omega^*$ is of weak type $L\log\log L(\mathbb{R}^d)$. Furthermore, for $w\in A_1$ and $\Omega\in…

We prove the weak type (1,1) estimate for maximal function of the truncated rough Hilbert transform considered in [9] and [10]

This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates for the weak gradient of the maximal function, which imply…

Let $\Omega_1,\Omega_2$ be functions of homogeneous of degree $0$ and $\vec\Omega=(\Omega_1,\Omega_2)\in L\log L(\mathbb{S}^{n-1})\times L\log L(\mathbb{S}^{n-1})$. In this paper, we investigate the limiting weak-type behavior for bilinear…

For a strictly stationary sequence of $\mathbb{R}_{+}^{d}$--valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variation and weak dependence conditions. The limit process is an…

We prove necessary and sufficient conditions for the weak-$L^p$ boundedness, for $p \in (1,\infty)$, of a maximal operator on the infinite-dimensional torus. In the endpoint case $p=1$ we obtain the same weak-type inequality enjoyed by the…

Let $H^{(u)}$ be the Hilbert transform along the parabola $(t, ut^2)$ where $u\in \mathbb R$. For a set $U$ of positive numbers consider the maximal function $\mathcal{H}^U \!f= \sup\{|H^{(u)}\! f|: u\in U\}$. We obtain an (essentially)…

For any operator $T$ whose bilinear form can be dominated by a sparse bilinear form, we prove that $T$ is bounded as a map from $L^1(\widetilde{M}w)$ into weak--$L^1(w)$. Our main innovation is that $\widetilde{M}$ is a maximal function…

The aim of this paper is to show that the discrete maximal function $$\mathcal{M}_{h}f(x)=\sup_{N\in\mathbb{N}}\frac{1}{|\mathbf{N}_{h}\cap[1, N]|}\Big|\sum_{n\in \mathbf{N}_{h}\cap[1, N]}f(x-n)\Big|,\ \ \mbox{for $x\in\mathbb{Z}$},$$ is of…

We study geodesics for plurisubharmonic functions from the Cegrell class ${\mathcal F}_1$ on a bounded hyperconvex domain of ${\mathbb C}^n$ and show that, as in the case of metrics on K\"{a}hler compact menifolds, they linearize an energy…

In this paper, our aim is to show some mean value inequalities for the Fox-Wright functions, such as Tur\'an--type inequalities, Lazarevi\'c and Wilker--type inequalities. As applications we derive some new type inequalities for…

We improve the Gagliardo-Nirenberg inequality \[ \|\varphi\|_{L^q(\mathbb{R}^n)} \le C \|\nabla\varphi\|_{L^r(\mathbb{R}^n)} \mathcal{L}^{-(\frac 1q - \frac{n-r}{rn})} (\|\nabla\varphi\|_{L^r(\mathbb{R}^n)}), \] $r=2$,…

As shown in [A1], the lowest constants appearing in the weak type (1,1) inequalities satisfied by the centered Hardy-Littlewood maximal operator associated to certain finite radial measures, grow exponentially fast with the dimension. Here…

In [J. Bures, R. Lavicka, V. Soucek, Elements of quaternionic analysis and Radon transform, Textos de Matematica 42, Departamento de Matematica, Universidade de Coimbra, 2009], the authors describe a link between holomorphic functions…

It is well known that the weak ($1,1$) bounds doesn't hold for the strong maximal operators, but it still enjoys certain weak $L\log L$ type norm inequality. Let $\Phi_n(t)=t(1+(\log^+t)^{n-1})$ and the space $L_{\Phi_n}({\mathbb R^{n}})$…

For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…