Let X be a complex Banach space and let Bloch(X) denote the space of X-valued analytic functions on the unit disc verifying that sup|z|<1(1−|z|)||f ′(z)|| < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y is said to be an operator-valued multiplier between Bloch(X) and 1(Y ) if the map ∑∞ n=0 xnz n → (Tn(xn))n defines a bounded linear operator from Bloch(X) into 1(Y )...

We extend the localization techniques of Bloch to simplicial spaces. As applications, we give an extension of Bloch’s localization theorem for the higher Chow groups to schemes of finite type over a regular scheme of dimension one (including mixed characteristic) and, relying on a fundamental result of Friedlander-Suslin, we globalize the Bloch-Lichtenbaum spectral sequence to give a spectral s...

The aim of the present paper is to completely characterize boundedness and compactness a sum operator defined by some more complex products composition, multiplication, mth iterated radial derivative operators from Bloch-type spaces weighted-type on unit ball. In applications, all ball are also characterized.

Let $ \mu be a positive Borel measure on the interval [0, 1) $. The Hankel matrix {\mathcal H}_\mu = (\mu_{n+k})_{n, k\geq 0} with entries \mu_{n, k} \mu_{n+k} induces operator H}_\mu(f)(z) \sum\limits_{n 0}^\infty\left(\sum\limits_{k 0}^\infty\mu_{n,k}a_k\right)z^n space of all analytic functions f(z) \sum^\infty_{n 0}a_nz^n in unit disk {\mathbb{D}} In this paper, we characterize boundedness ...