Related papers: Integration and differentiation operators between …

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…

In this research we introduce the Banach space valued $H^p$ spaces with $A_p$ weight, and prove the following results: Let $\mathbb{A}$ and $\mathbb{B}$ Banach spaces, and $T$ be a convolution operator mapping $\mathbb{A}$-valued functions…

In this paper we investigate compactness of weighted Lambert type operators between two Lp spaces

We define a scale of weighted Morrey spaces which contains different weighted versions appearing in the literature. This allows us to obtain weighted estimates for operators in a unified way. In general, we obtain results for weights of the…

We characterize the spectrum and essential spectrum of "essentially linear fractional" composition operators acting on the Hardy space H-two of the open unit disc U. When the symbols of these composition operators have Denjoy-Wolff point on…

Let M be an N-function satisfying the $\Delta_2$- condition, let $\omega, \vp$ be two other functions, $\omega\ge 0$. We study Hardy-type inequalities \[ \int_{\rp} M(\omega (x)|u(x)|) {\rm exp}(-\vp (x))dx \le C\int_{\rp} M(|u'(x)|) {\rm…

We characterize the sufficient conditions which three weight functions $u$ and $v_{1}, v_{2}$ satisfy ensure the boundedness of the Hardy operator with variable limits on product space. The corresponding bound is explicitly worked out.…

In this paper, we present a solution to the inequality $$ \bigg( \int_0^{\infty} \bigg( \int_x^{\infty} \bigg( \int_0^t h \bigg)^q w(t)\,dt \bigg)^{r / q} u(x)\,ds \bigg)^{1/r}\leq C \, \bigg( \int_0^{\infty} h^p v \bigg)^{1 / p}, \quad h…

In this paper we investigate the boundedness of classical operators, namely the Hardy-Littlewood maximal operator, fractional integral operators, and Calderon-Zygmund operators, on generalized weighted Morrey spaces and generalized weighted…

We establish weighted extrapolation theorems in classical and grand Lorentz spaces. As a consequence we have the weighted boundedness of operators of Harmonic Analysis in grand Lorentz spaces. We treat both cases: diagonal and off-diagonal…

We give a systematic study on the Hardy spaces of functions with values in the non-commutative $L^p$-spaces associated with a semifinite von Neumann algebra ${\cal}M.$ This is motivated by the works on matrix valued Harmonic Analysis…

Let $M$ be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces $H^p$ of differential forms on $M$ and give various characterizations of them, including an atomic decomposition.…

We characterize the spectrum of Hausdorff operators on weighted Bergman and power weighted Hardy spaces of the upper half-plane.

Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces $H^p$ of the upper half-plane and we review how their Fredholm properties can be studied in terms…

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of $\mathbb{C}.$ In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not…

We characterize a three-weight inequality for an iterated discrete Hardy-type operator. In the case when the domain space is a weighted space $\ell^p$ with $p\in(0,1]$, we develop characterizations which enable us to reduce the problem to…

We explore the connection between $p$-regular operators on Banach function spaces and weighted $p$-estimates. In particular, our results focus on the following problem. Given finite measure spaces $\mu$ and $\nu$, let $T$ be an operator…

Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…

We use the notion of radial derivative to introduce composition-differentiation operators on the Hardy and Bergman spaces of the unit ball and the polydisk. We seek for necessary and sufficient conditions on the inducing functions to ensure…

In this paper one-weight inequalities with general weights for Riemann-Liouville transform and $ n-$ dimensional fractional integral operator in variable exponent Lebesgue spaces defined on $\mathbb{R}^{n}$ are investigated. In particular,…