Related papers: The Mittag Leffler space & its Littlewood-Paley Id…

We present important characterizations of the Weighted Composition Operator over the Mittag Leffler space of entire functions. These characterizations include the Hilbert-Schmidt and Unitary char-acterizations of the Weighted Composition…

We study the numerical range of the Weighted Composition Operator over the Mittag-Leffler space of entire functions.

Let $L:=-\Delta+V$ be the Schr\"{o}dinger operator on $\mathbb{R}^n$ with $n\geq 3$, where $V$ is a non-negative potential which belongs to certain reverse H\"{o}lder class $RH_q(\mathbb{R}^n)$ with $q\in (n/2,\,\infty)$. In this article,…

It is shown that a large class of properties coincide for weighted composition operators on a large class of weighted VMOA spaces, including the ones with logarithmic weights and the ones with standard weights $(1-|z|)^{-c}, \ 0\leq c<…

We consider certain Littlewood-Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for H\"ormander's…

We obtain a complete characterization of the entire functions $g$ such that the integral operator $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ is bounded or compact, on a large class of Fock spaces $\mathcal{F}^\phi_p$, induced by…

We study decay and smoothness properties for eigenfunctions of compact localization operators. Operators with symbols a in the wide modulation space M^{p,\infty} (containing the Lebesgue space L^p), p<\infty, and windows \f_1,\f_2 in the…

We discuss compactness of the d-bar-Neumann operator in the setting of weighted L^2-spaces on C^n.$ For this purpose we use a description of relatively compact subsets of L^2- spaces. We also point out how to use this method to show that…

We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties…

In this paper, we prove the boundedness of the multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces, then we give the boundedness and weak-type $L\log L$ estimates for the commutators of multilinear…

Let $X$ be a space of homogeneous type. Assume that $L$ is an non-negative second-order self-adjoint operator on $L^2\left(X\right)$ with (heart) kernel associated to the semigroup $e^{ - tL}$ that satisfies the Gaussian upper bound. In…

In this paper, we give a Littlewood-Paley characterization for the H\"older-Zygmund spaces $\mathcal{C}^{\sigma}(G)$ ($0< \sigma <\infty$) on a stratified Lie group $G$.

We define the vector-valued, matrix-weighted function spaces $\dot{F}^{\alpha q}_p(W)$ (homogeneous) and $F^{\alpha q}_p(W)$ (inhomogeneous) on $\mathbb{R}^n$, for $\alpha \in \mathbb{R}$, $0<p<\infty$, $0<q \leq \infty$, with the matrix…

Let $L_{1}$ and $L_{2}$ be non-negative self-adjoint operators acting on $L^{2}(X_{1})$ and $L^{2}(X_{2})$, respectively, where $X_{1}$ and $X_{2}$ are spaces of homogeneous type. Assume that $L_{1}$ and $L_{2}$ have Gaussian heat kernel…

We study the mapping property of the commutator of bilinear Hardy-Littlewood maximal operator in homogeneous Triebel-Lizorkin space. We also show that the commutator of bilinear Hardy-Littlewood maximal operator is a compact operator acting…

In this paper, the object of our investigation is the following Littlewood-Paley square function $g$ associated with the Schr\"odinger operator $L=-\Delta +V$ which is defined by:…

In this paper, we prove that the original Littlewood-Paley $g$-functions can be used to characterize Bergman spaces as well.

Via the new weight function $A_{\vec p}^{\theta }(\varphi )$, the authors introduce a new class of multilinear Littlewood--Paley $g_{\lambda}^{*}$ functions and establish the boundedness on weighted Lebesgue spaces. In addition, the authors…

We prove an analogue to the Cayley identity for an arbitrary self-adjoint operator in a Hilbert space. We also provide two new ways to characterize vectors belonging to the singular spectral subspace in terms of the analytic properties of…

Let $0<\alpha<2$, $\beta>0$ and $\alpha/2<|s|\leq 1$. In a previous work, we obtained all possible values of the Lebesgue exponent $p=p(\gamma)$ for which the Fourier transform of $ E_{\alpha,\beta}(e^{\dot{\imath}\pi s} |\cdot|^{\gamma} )$…