Related papers: $L^p$ Regularity of Weighted Szeg\"o Projections o…

We show weighted non-autonomous $L^q(L^p)$ maximal regularity for families of complex second-order systems in divergence form under a mixed regularity condition in space and time. To be more precise, we let $p,q \in (1,\infty)$ and we…

Let $\mathcal{D}$ be the class of radial weights on the unit disk which satisfy both forward and reverse doubling conditions. Let $g$ be an analytic function on the unit disk $\mathbb{D}$. We characterize bounded and compact Volterra type…

Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient…

In this paper, we study an extremal problem concerning best approximation in the Hardy space $H^1$ on the unit disk $\mathbb D$. Specifically, we consider weighted combinations of the Cauchy-Szeg\"o kernel and its derivative, parametrized…

Using {\it weighted traces} which are linear functionals of the type $$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$ defined on the whole algebra of (classical) pseudo-differential operators (P.D.O.s) and where $Q$ is some…

We study weighted altered Ces\`aro and Copson spaces, which is non-ideal enlargement of the usual spaces. We give full characterization of dual spaces for the spaces.

Let $G$ be a locally compact, compactly generated group of polynomial growth and let $\omega$ be a weight on $G$. Under proper assumptions on the weight $\omega$, the Banach space $L^p(G,\omega)$ is a Banach \ast-algebra. In this paper we…

We consider the problem of $L^1$ (un)boundedness for a wide class of orthogonal projections, including Bergman projections on domains in complex manifolds and Szeg\"o projections on abstract CR manifolds.

We prove some isoperimetric type inequalities for real harmonic functions in the unit disk belonging to the Hardy space $h^p$, $p>1$ and for complex harmonic functions in $h^4$. The results extend some recent results on the area. Further we…

We determine exactly when two classes of integral operators are bounded on weighted $L^p$ spaces over the Siegel upper half-space.

For a given second-order linear elliptic operator $L$ which admits a positive minimal Green function, and a given positive weight function $W$, we introduce a family of weighted Lebesgue spaces $L^p(\phi_p)$ with their dual spaces, where…

In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differential operators within the framework of weighted mixed norm…

We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on $\ell^p(\mathbb Z)$, $p\geq 1$. Our method uses properties of the difference set of a set with positive upper…

Let $p\in(0,\infty)$, $q\in[1,\infty)$, $s\in\mathbb Z_+$, and $W$ be an $A_p$-matrix weight, which in the scalar case is exactly a Muckenhoupt $A_{\max\{1,p\}}$ weight. In this article, by using the reducing operators of $W$, we introduce…

In this paper we study boundedness and detailed spectral properties for the Ces\`aro-Hardy operator and some generalizations in $L^p[0,1]$. The study employs $C_0$-semigroup theory, expressing the Ces\`aro-Hardy operators and their dual…

In this paper, we characterize the weighted local Hardy spaces $h^p_\rho(\omega)$ related to the critical radius function $\rho$ and weights $\omega\in A_{\infty}^{\rho,\,\infty}(\mathbb{R}^{n})$ which locally behave as Muckenhoupt's…

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calder\'on--Zygmund type operators $T_\theta$ in these new weighted spaces. Furthermore, the…

In this paper we study weighted Hardy-Sobolev spaces of vector valued functions analytic on double-napped cones of the complex plane. We introduce these spaces as a tool for complex scaling of linear ordinary differential equations with…

We introduce a new class of weighted local approximate atoms including classical weighted local atoms. Then we further obtain the weighted local approximate atomic decompositions of weighted local Hardy spaces $h_{\omega} ^p(R^n)$ with…

We present factorizations of weighted Lebesgue, Ce\-s\` aro and Copson spaces, for weights satisfying the conditions which assure the boundedness of the Hardy's integral operator between weighted Lebesgue spaces. Our results enhance, among…