Related papers: Properties of singular integral operators $S_{\alp…

We consider a class of singular Schr\"odinger operators $H$ that act in $L^2(0,\infty)$, each of which is constructed from a positive function $\phi$ on $(0,\infty)$. Our analysis is direct and elementary. In particular it does not mention…

In this note, we completely characterize complex symmetric weighted composition differentiation operator on the Hardy space $H^2$ with respect to the conjugation operator $C_{\lambda,\alpha}$. Meanwhile, the normal and self-adjoint of the…

In this paper we introduce and prove some properties of $(\alpha;\beta)$-normal operators according to semi-Hilbertian space structures. Furthermore we s,ate various inequalities between the A-operator norm and A-numerical radius of…

We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels…

For $\alpha\in [1,2)$ we consider operators of the form $$L f(x)=\int_{R^d} [f(x+h)-f(x)-1_{(|h|\leq 1)} \nabla f(x)\cdot h] \frac{A(x,h)}{|h|^{d+\alpha}}$$ and for $\alpha\in (0,1)$ we consider the same operator but where the $\nabla f$…

We characterize the domain of the Schr\"odinger operators $S=-\Delta+c|x|^{-\alpha}$ in $L^p(\mathbb{R}^N)$, with $0<\alpha<2$ and $c\in\mathbb{R}$. When $\alpha p< N$, the domain characterization is essentially known and can be proved…

In this paper, we shall find the order of starlikeness and convexity for integral operators \begin{equation*} \mathbb{F}_{\alpha _{j},\beta _{j},\lambda _{j},\zeta }(z)=\left\{ \zeta \int\limits_{0}^{z}t^{\zeta -1}\prod_{j=1}^{n}\left(…

We show that a Schr\"odinger operator $A_{\delta, \alpha}$ with a $\delta$-interaction of strength $\alpha$ supported on a bounded or unbounded $C^2$-hypersurface $\Sigma \subset \mathbb{R}^d$, $d\ge 2$, can be approximated in the norm…

We prove that a Volterra-type integral operator $T_gf(z) = \int_0^z f(\zeta)g'(\zeta)d\zeta, \, z \in \mathbb D,$ defined on Hardy spaces $H^p, \, 1 \le p < \infty,$ fixes an isomorphic copy of $\ell^p,$ if the operator $T_g$ is not…

For entire operators and entire operators in the generalized sense, we provide characterizations based on the spectra of their selfadjoint extensions. In order to obtain these spectral characterizations, we discuss the representation of a…

Let $\Omega$ be a function of homogeneous of degree zero and vanish on the unit sphere $\mathbb {S}^n$. In this paper, we investigate the limiting weak-type behavior for singular integral operator $T_\Omega$ associated with rough kernel…

We characterize the (essentially) decreasing sequences of positive numbers $\beta$ = ($\beta$ n) for which all composition operators on H 2 ($\beta$) are bounded, where H 2 ($\beta$) is the space of analytic functions f in the unit disk…

Let $A$ be a Banach space, $p>1$, and $1/p+1/q=1$. If a sequence $a=(a_i)$ in $A$ has a finite $p$-sum, then the operator $\Lambda_a:\ell^q\to A$, defined by $\Lambda_a(\beta)=\sum_{i=1}^\infty \beta_i a_i, \beta=(\beta_i)\in \ell^q$, is…

Let $\alpha\in (0, 1]$, $\beta\in [0, n)$ and $T_{\Omega,\beta}$ be a singular or fractional integral operator with homogeneous kernel $\Omega$. In this article, a CMO type space ${\rm CMO}_\alpha(\mathbb R^n)$ is introduced and studied. In…

This is a continuation of our previous research about an oscillatory integral operator $T_{\alpha, \beta}$ on compact manifolds $\mathbb{M}$. We prove the sharp $H^{p}$-$L^{p,\infty}$ boundedness on the maximal operator $T^{*}_{\alpha,…

This paper continues the study, initiated in the works {MOV} and {MOPV}, of the problem of controlling the maximal singular integral $T^{*}f$ by the singular integral $Tf$. Here $T$ is a smooth homogeneous Calder\'on-Zygmund singular…

We present upper estimates for the number of negative eigenvalues of two-dimensional Schroedinger operators with potentials generated by Ahlfors regular measures of arbitrary dimension $\alpha\in (0, 2]$.The estimates are given in terms of…

In this paper we study the Bergman-Toeplitz operator $T_{\psi}$ induced by $\psi(w) = K_{\Omega}^{-\alpha}(w,w)d_{\Omega}^{\beta}(w)$ with $\alpha, \beta \geq 0$ acting from a weighted $L^p$-space $L_a^p(\Omega)$ to another one…

We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…

Let $\,I\subseteq\mathbb{R}\,$ be an interval and $\,\beta:\,I\rightarrow\,I\,$ a strictly increasing and continuous function with a unique fixed point $\,s_0\in I\,$ which satisfies $\,(s_0-t)(\beta(t)-t)\geq 0\,$ for all $\,t\in I$, where…