Related papers: Two Weight Inequalities for Riesz Transforms: Unif…

Two-weight norm estimates for the double Hardy transforms and strong fractional maximal functions are established in variable exponent Lebesgue spaces. Derived conditions are simultaneously necessary and sufficient in the case when the…

We propose iterative inversion algorithms for weighted Radon transforms $R_W$ along hyperplanes in $R^3$. More precisely, expandingthe weight $W = W (x, \theta), x \in R^3 , \theta \in S^2$ , into the series of spherical harmonics in…

It is proved that each bounded injective bilateral weighted shift $W$ satisfying the equality $W^{*n}W^{n}=(W^{*}W)^{n}$ for some integer $n\geq 2$ is quasinormal. For any integer $n\geq 2$, an example of a bounded non-quasinormal weighted…

We study the Caffarelli-Kohn-Nirenberg type inequalities in the case of $p=1$ and generalize them adopting weight functions $w(|x|)$ on $R^n$ with $w(t)$ in ${W}(R_+)$. Here ${W}(R_+)$ is a general class of weight functions on $R_+$…

In this paper we show weighted estimates in mixed norm spaces for the Riesz transform associated with the harmonic oscillator in spherical coordinates. In order to prove the result we need a weighted inequality for a vector-valued extension…

For $1<p<\infty$, we establish the $L_{p}$ boundedness of the maximal Riesz transforms in terms of the Riesz transforms on quantum tori $L_{p}(\mathbb{T}^{d}_{\theta})$, and quantum Euclidean space $L_{p}(\mathbb{R}^{d}_{\theta})$. In…

It is shown that, with the only exception of $n=2$, the Einstein-Hilbert action in $n+D+d$ dimensions, with $n$ times, is invariant under the duality transformation $a\to \frac{1}{a}$ and $b\to \frac{1}{b}$, where $a$ is a…

We obtain convolution inequalities in Lebesgue and Lorentz spaces with power weights when the functions involved are assumed to be radially symmetric. We also present applications of these results to inequalities for Riesz potentials of…

We consider two weight $L^{p}\to L^{q}$-inequalities for dyadic shifts and the dyadic square function with general exponents $1<p,q<\infty$. It is shown that if a so-called quadratic $\mathscr{A}_{p,q}$-condition related to the measures…

For a Hilbert space valued martingale $(f_n)$ and an adapted sequence of positive random variables $(w_n)$, we show the weighted Davis type inequality \[ \mathbb{E} \Bigl( |f_0| w_0 + \frac{1}{4} \sum_{n=1}^{N} \frac{|df_n|^2}{f^*_n} w_n…

W prove a dimension-free estimate for the $L^2(\mathbb{R}^d)$ norm of the maximal truncated Riesz transform in terms of the $L^2(\mathbb{R}^d)$ norm of the Riesz transform. Consequently, the vector of maximal truncated Riesz transforms has…

In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…

We establish a new global endpoint Sobolev inequality for measures that extends the classical theorem of Meyers-Ziemer by placing a maximal function on the right-hand side. This result has several significant consequences. It extends…

Let $M$ be a complete Riemannian manifold satisfying the doubling volume condition for geodesic balls and $L^q$ scaled Poincar\'e inequalities on suitable remote balls for some $q<2$. We prove the inequality $\left\Vert…

We derive sharp Adams inequalities with exact growth condition for the Riesz potential as well as more general Riesz-like potentials on R^n. We also obtain Moser-Trudinger inequalities with exact growth condition for the fractional…

Let ${\mathscr{L}}=-\text{div}A\nabla$ be a uniformly elliptic operator on $\mathbb{R}^n$, $n\ge 2$. Let $\Omega$ be an exterior Lipschitz domain, and let ${\mathscr{L}}_D$ and ${\mathscr{L}}_N$ be the operator ${\mathscr{L}}$ on $\Omega$…

Let $\Omega\subsetneq\mathbb R^{n+1}$ be open and let $\mu$ be some measure supported on $\partial\Omega$ such that $\mu(B(x,r))\leq C\,r^n$ for all $x\in\mathbb R^{n+1}$, $r>0$. We show that if the harmonic measure in $\Omega$ satisfies…

The Dirichlet boundary-value problem and isoperimetric inequalities for positive definite regular solutions of the vacuum Einstein equations are studied in arbitrary dimensions for the class of metrics with boundaries admitting a U(1)…

Given a domain D in R^d with mild geometric measure theoretic assumptions on its boundary, we show that boundedness of the principal value Riesz tranforms (witn kernel of homogeneity -(d-1)) on H\"older spaces of order alpha on the boundary…

Let $M_1$, $\cdots$, $M_\ell$ be complete, connected and non-collapsed manifolds of the same dimension, where $2\le \ell\in\mathbb{N}$, and suppose that each $M_i$ satisfies a doubling condition and a Gaussian upper bound for the heat…