Related papers: Weighted norm inequalities for convolution and Rie…
This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a…
In this dissertation we explore the $[L^{\mathrm{p}},\ L^{q}]$-boundedness of certain integral operators on weighted spaces on cones in ${\mathbb R}^{n}.$ These integral operators are of the type $\displaystyle \int_{V}k(x,\ y)f(y)dy$…
The purpose of this paper is threefold. First the natural extension of Riesz potentials to the context of quasi metric measure spaces for the class of upper doubling measures are studied on Lebesgue spaces, obtaining necessary and…
In the 1970s Muckenhoupt and Wheeden made several conjectures relating two weight norm inequalities for the Hardy-Littlewood maximal operator to such inequalities for singular integrals. Using techniques developed for the recent proof of…
In this paper we study two different weighted isoperimetric inequalities. In the first part of the paper we prove a sharp stability result for the isoperimetric inequality with a log-convex weight. In the second part we analize the behavior…
In this article, we study the problem of obtaining Lebesgue space inequalities for the Fourier restriction operator associated to rectangular pieces of the paraboloid and perturbations thereof. We state a conjecture for the dependence of…
In this paper we present some inequalities involving operator decreasing functions and operator means. These inequalities provide some reverses of operator Acz\'el inequality dealing with the weighted geometric mean.
In this paper we introduce a new technique for proving norm inequalities in operator ideals with an unitarily invariant norm. Among the well known inequalities which can be proved with this technique are the L\"owner-Heinz inequality,…
We prove weighted $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators in higher dimensions. The vector-valued extensions of these inequalities are also given.
In this paper, we obtain non-symmetric and symmetric versions of the classical Heisenberg-Pauli-Weyl uncertainty principle in Lebesgue spaces with power weights.
We consider a generalization of the Riesz operator in $R^d$ and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of $T1$ theorem for…
Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical…
In this work we obtain a transference theorem for Lebesgue spaces with $A_{\infty }$ weights, namely, starting from some uniform-norm inequalities it is possible to obtain similar inequalities in Lebesgue spaces with $A_{\infty }$ weights.…
We derive criteria governing two-weight estimates for multilinear fractional integrals and appropriate maximal functions. The two and one weight problems for multi(sub)linear strong fractional maximal operators are also studied; in…
In this paper, we show a weighted Hardy inequality in a limiting case for functions in weighted Sobolev spaces with respect to an invariant measure. We also prove that the constant in the left-hand side of the inequality is optimal. As…
We consider the Hardy-Littlewood-Sobolev inequality on mixed-norm Lebesgue spaces. We give a complete characterization of indices $\vec p$ and $\vec q$ such that the Riesz potential is bounded from $L^{\vec p}$ to $L^{\vec q}$, including…
We study $\ell^r$-valued extensions of linear operators defined on Lebesgue spaces with variable exponent. Under some natural (and usual) conditions on the exponents, we characterize $1\leq r\leq \infty$ such that every bounded linear…
We study weighted norm inequalities of $(1,q)$- type for $0<q<1$, $\Vert \mathbf{G} \nu \Vert_{L^q(\Omega, d \sigma)} \le C \, \Vert \nu \Vert, \quad \text{for all positive measures $\nu$ in $\Omega$},$ along with their weak-type…
Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where $\Delta $ is the Laplacian operator on $\rz$, while the nonnegative potential $V$ belongs to certain reverse H\"{o}lder class. In this paper, we establish some weighted norm…
We characterize a weighted norm inequality which corresponds to the embedding of a class of absolutely continuous functions into the fractional order Sobolev space. The auxiliary result of the paper is of independent interest. It comprises…