We study the Hardy space of translated Dirichlet series $${\mathscr {H}}_{+}$$ . It consists on those $$\sum a_n n^{-s}$$ such that for some (equivalently, every) $$1 \le p < \infty $$ , translation {a_{n}}n^{-(s+\frac{1}{\sigma })}$$ belongs to {H}}^{p}$$ every $$\sigma >0$$ prove this set, endowed with topology induced by seminorms $$\left\{ \Vert \cdot _{2,k}\right\} _{k\in {\mathbb {N}}}$$ ...

The role of Liouville operators in the study dynamical systems through use occupation measures has been an active area research control theory over past decade. This manuscript investigates Hardy space, which encode complex ordinary differential equations operator a reproducing kernel Hilbert space.

In this paper we state the following weighted Hardy type inequality for any functions $ \varphi in a Sobolev space and weight \mu of quite general \begin{document}$ \begin{align*} c_{N, \mu} \int_{ \mathbb{R}^N}V\, \varphi^2\mu(x)dx\le \mathbb{R}^N}|\nabla \varphi|^2\mu(x)dx +C_\mu \mathbb{R}^N}W \varphi^2\mu(x)dx, \end{align*} $\end{document} where V is multipolar potential W bounded function ...

A result on bi-shadowing for continuous single-valued contractions satisfying certain conditions has been given by AlBadarneh (2015). In this paper, we continue the discussion of asymptotic properties of trajectories for mappings belonging to more subclasses of almost contractions. In particular, we prove that Zamfirescu Mappings, QuasiContractions, Generalised Contractions, and Hardy-Rogers Co...