Related papers: Mixed-norm Herz-slice Spaces and Their Application…

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

Let $({\mathcal X},d,\mu)$ be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions. Let $\rho\in (1,\infty)$, $0<p\le1\le q\le\infty$, $p\neq q$, $\gamma\in[1,\infty)$ and…

We present sharp lower bounds for the A-numerical radius of semi-Hilbertian space operators. We also present an upper bound. Further we compute new upper bounds for the $B$-numerical radius of $2 \times 2$ operator matrices where $B =…

Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.

Let $X$ be a ball quasi-Banach function space satisfying some minor assumptions. In this article, the authors establish the characterizations of $H_X(\mathbb{R}^n)$, the Hardy space associated with $X$, via the Littlewood--Paley…

In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below, positive injectivity radius and spectral gap b. We introduce a sequence X^1(M), X^2(M), ... of new Hardy spaces on M,…

Let ${\mathcal X}$ be an RD-space, which means that ${\mathcal X}$ is a space of homogenous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in ${\mathcal X}$. In this paper, the…

The aim of this paper is to study the sharp bounds of rough Hausdorff operators on the product of Herz, central Morrey and Morrey-Herz spaces with both power weights and Muckenhoupt weights on the Heisenberg group. Especially, by applying…

Let $(\mathcal X, d,\mu)$ be an RD-space, and let $\rho$ be an admissible function on $\mathcal X$. We establish necessary and sufficient conditions for the boundedness of a new class of generalized Calder\'on-Zygmund operators of log-Dini…

The paper introduces unbounded antilinear operators on Hilbert spaces and develops their fundamental theory. In particular, we establish a closed range theorem, a polar decomposition theorem, and the convexity of the numerical range for…

We establish a complete theory of the flag Hardy space on the Heisenberg group $\mathbb H^{n}$ with characterisations via atomic decompositions, area functions, square functions, maximal functions and singular integrals. We introduce…

Let $X$ be a ball quasi-Banach function space satisfying some mild assumptions and $H_X(\mathbb{R}^n)$ the Hardy space associated with $X$. In this article, the authors introduce both the Hardy space $H_X(\mathbb{R}^{n+1}_+)$ of harmonic…

A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration…

In this work we obtain boundedness on weighted variable Lebesgue spaces of some maximal functions that come from the localized analysis considering a critical radius function. This analysis appears naturally in the context of the…

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 estimate an operator norm of dilation operators on block spaces ($\mathfrak{B}_{r,\alpha}(\mathbb{Q}_p)$) over $p$-adic field. With this estimate, we establish the boundedness of $p$-adic Hardy-Hilbert type integral…

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 study the bicomplex version of weighted Hardy spaces. Further, we describe reproducing kernels for the bicomplex weighted Hardy spaces. In particular, we generalize some results which holds for the classical weighted Hardy…

We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and…

Let $\vec{p}\in(0,\infty)^n$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, via the non-tangential grand maximal function, the authors first introduce the anisotropic mixed-norm Hardy spaces…