Related papers: Sharp bounds for Hardy-type operators on mixed rad…
This paper investigates the $L^p$-bounds of wave operators for higher-order Schr\"odinger operators $H = (-\Delta)^m + V$ on $\mathbb{R}^n$, with $m \ge 2$ and real-valued decaying potentials $V$. Our main objective is to establish the…
One defines a non-homogeneous space $(X, \mu)$ as a metric space equipped with a non-doubling measure $\mu$ so that the volume of the ball with center $x$, radius $r$ has an upper bound of the form $r^n$ for some $n> 0$. The aim of this…
We show that the Hardy-Littlewood maximal operator is bounded on a reflexive variable Lebesgue space $L^{p(\cdot)}$ over a space of homogeneous type $(X,d,\mu)$ if and only if it is bounded on its dual space $L^{p'(\cdot)}$, where…
In this paper, we establish a general weighted Hardy type inequality for the $% p-$Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results for different weights. Furthermore, we present…
It is well known that the Hilbert matrix operator $\mathcal {H}$ is bounded from $H^{\infty}$ to the mean Lipschitz spaces $\Lambda^{p}_{\frac{1}{p}}$ for all $1<p<\infty$. In this paper, we prove that the range of Hilbert matrix operator…
In this paper, we investigate the $H^p(G) \rightarrow L^p(G)$, $0< p \leq 1$, boundedness of multiplier operators defined via group Fourier transform on a graded Lie group $G$, where $H^p(G)$ is the Hardy space on $G$. Our main result…
We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $\Delta_\lambda$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained…
In this paper a two weight criterion for multidimensional geometric mean operator in variable exponent Lebesgue space is proved. Also, we found a criterion on weight functions expressing one-dimensional Hardy inequality via a certain…
Results of Liflyand and collaborators on the boundedness of Hausdorff operators on the Hardy space $H^1$ over finite-dimensional real space generalized to the case of locally compact groups that are spaces of homogeneous type. Special cases…
By using a suitable transform related to Sobolev inequality, we investigate the sharp constants and optimizers in radial space for the following weighted Caffarelli-Kohn-Nirenberg-type inequalities: \begin{equation*}…
We study the approximation numbers of weighted composition operators $f\mapsto w\cdot(f\circ\varphi)$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers…
In this paper, we give necessary and sufficient conditions for the boundedness of rough Hausdorff operators on Herz, Morrey and Morrey-Herz spaces with absolutely homogeneous weights. Especially, the estimates for operator norms in each…
In this paper, we obtain the weighted boundedness for the local multi(sub)linear Hardy-Littlewood maximal operators and local multilinear fractional integral operators associated with the local Muckenhoupt weights on Gaussian measure…
In this paper, we characterize the convexity of the Berezin range for finite-rank operators acting on the weighted Hardy space $\mathcal{H}_\gamma (\mathbb{D})$ over the unit disc $\mathbb{D}$. We provide a complete classification in terms…
For a pointwise multiplier $\varphi$ of the Hardy-Sobolev space $H^2_\beta$ on the open unit ball $\bn$ in $\cn$, we study spectral properties of the multiplication operator $M_\varphi: H^2_\beta\to H^2_\beta$. In particular, we compute the…
Beltran \& Cladek~\cite{BC} use $L^r$ to $L^s$ bounds to prove sparse form bounds for pseudodifferential operators with H\"ormander symbols in $S^m_{\rho,\delta}$ up to, but not including, the sharp end-point in decay $m$. We further…
This paper establishes new upper bounds for the $A$-numerical radius of operator matrices in semi-Hilbertian spaces by leveraging the $A$-Buzano inequality and developing refined techniques for operator matrices. We present several sharp…
In this paper, we introduce a discrete version of weighted Morrey spaces, and discuss the inclusion relations of these spaces. In addition, we obtain the boundedness of discrete weighted Hardy-Littlewood maximal operators on discrete…
We consider the global Morrey-type spaces with variable exponents and general function defining these spaces. In the case of unbounded sets, we prove boundedness of the Hardy-Littlewood maximal operator, potential type operator in these…
In this paper we study the behavior of some harmonic analysis operators associated with the discrete Laplacian $\Delta_d$ in discrete Hardy spaces $\mathcal H^p(\mathbb Z)$. We prove that the maximal operator and the Littlewood-Paley $g$…