相关论文: Hilbert-type operator induced by radial weight on …

Motivated by the canonical decomposition of contractions on Hilbert spaces, we investigate when contractive Toeplitz operators on vector-valued Hardy spaces on the unit disc admit a non-zero reducing subspace on which its restriction is…

For a given bounded positive (semidefinite) linear operator $A$ on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$, we consider the semi-Hilbertian space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle_A…

In this paper we characterize the inequality \begin{equation*} \bigg( \int_0^{\infty} \bigg( \int_0^x \big[ T_{u,b}f^* (t)\big]^r\,dt\bigg)^{\frac{q}{r}} w(x)\,dx\bigg)^{\frac{1}{q}} \le C \, \bigg( \int_0^{\infty} \bigg( \int_0^x [f^*…

We show that every non-compact weighted composition operator $f \mapsto u\cdot (f\circ\phi)$ acting on a Hardy space $H^p$ for $1 \leq p < \infty$ fixes an isomorphic copy of the sequence space $\ell^p$ and therefore fails to be strictly…

Let $T$ be a pseudo-differential operator whose symbol belongs to the H\"ormander class $S^m_{\rho,\delta}$ with $0\leq \delta<1, 0< \rho\leq 1, \delta \leq \rho$ and $-(n+1)< m \leq - (n+1)(1-\rho)$. In present paper, we prove that if $b$…

Let $\omega$ and $\nu$ be radial weights on the unit disc of the complex plane, and denote $\sigma=\omega^{p'}\nu^{-\frac{p'}p}$ and $\omega_x =\int_0^1 s^x \omega(s)\,ds$ for all $1\le x<\infty$. Consider the one-weight inequality…

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi$ on Bergman type spaces $A_\omega^p $ with double weight $\omega$. Let $X=\{u\in H(D):…

We prove that the Markov-Stieltjes transform is a bounded non compact Hankel operator on Hardy space $H^p$ with Hilbert matrix with respect to the standard Schauder basis of $H^p$ and a bounded non compact operator on Lebesgue space…

We characterize the weights for the Stieltjes transform and the Calder\'on operator to be bounded on the weighted variable Lebesgue spaces $L_w^{p(\cdot)}(0,\infty)$, assuming that the exponent function $p(\cdot)$ is log-H\"older continuous…

Let $(X, d, \mu)$ be a space of homogeneous type, i.e. the measure $\mu$ satisfies doubling (volume) property with respect to the balls defined by the metric $d$. Let $L$ be a non-negative self-adjoint operator on $L^2(X)$. Assume that the…

Let $\mathcal{M}(\mathbb{R}^n)$ be the class of bounded away from one and infinity functions $p:\mathbb{R}^n\to[1,\infty]$ such that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space…

Let $\mu$ be a finite Borel measure on $[0,1)$. In this paper, we consider the generalized integral type Hilbert operator $$\mathcal{I}_{\mu_{\alpha+1}}(f)(z)=\int_{0}^{1}\frac{f(t)}{(1-tz)^{\alpha+1}}d\mu(t)\ \ \ (\alpha>-1).$$ The…

Let $(\mathcal{X},d,\mu)$ be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. Let $T$ be a Calder\'{o}n-Zygmund operator with kernel satisfying only the size condition and…

Let $f$ and $g$ be analytic on the unit disc $\mathbb{D}$. The integral operator $T_g$ is defined by $ T_g f(z) = \int_0^z f(t)g'(t)\,dt$, $z \in \mathbb{D}$. The problem considered is characterizing those symbols $g$ for which $T_g$ acting…

We consider the weighted $A^p(\omega)$ and $B_p(\omega)$ spaces of holomorphic functions on the polydisk (in the case of $p>1$). We prove some theorems about the boundedness of Toeplitz operators on weighted Besov spaces $B_p(\omega)$ and…

Hankel operators with anti-holomorphic symbols are studied for a large class of weighted Fock spaces on $\cn$. The weights defining these Hilbert spaces are radial and subject to a mild smoothness condition. In addition, it is assumed that…

In this paper, we first introduce $L^{\sigma_1}$-$(\log L)^{\sigma_2}$ conditions satisfied by the variable kernels $\Omega(x,z)$ for $0\leq\sigma_1\leq1$ and $\sigma_2\geq0$. Under these new smoothness conditions, we will prove the…

We study new weighted estimates for the 2-fold product of Hardy-Littlewood maximal operators defined by $M^{\otimes}(f,g):= MfMg$. This operator appears very naturally in the theory of bilinear operators such as the bilinear…

Let $\mu$ be a non-negative Radon measure on ${\mathbb R}^d$ which only satisfies the polynomial growth condition. Let ${\mathcal Y}$ be a Banach space and $H^1(\mu)$ the Hardy space of Tolsa. In this paper, the authors prove that a linear…

In this paper, we introduce a new type of parallelism for bounded linear operators on a Hilbert space $\big(\mathscr{H}, \langle \cdot ,\cdot \rangle\big)$ based on numerical radius. More precisely, we consider operators $T$ and $S$ which…