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 ...

The boundedness and the compactness of generalized weighted composition operators from weighted Bergman spaces into Zygmund-type spaces are investigated in this paper. Moreover, we give some estimates for the essential norm of these operators.

In this work we characterize boundedness and compactness of weighted composition operators acting between Dirichlet type spaces by using Carleson measures. We also find essential norm estimates for these operators.

We calculate the essential norm of some extensions of the generalized composition operators between kth weighted-type spaces on the unit disk in the complex plane, considerably extending some results in the literature.

In “Is the Frobenius Matrix Norm Induced?”, the authors ask whether the Frobenius and the norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the norm may not be induced. In this note, it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the norm is in fact induced on a particular matrix-v...

Weighted norm inequalities are proved for a rough homogeneous singular integral operator and its corresponding maximal truncated singular operator. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals.

Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.