Related papers: Meromorphic Optimal domain of Integral Operators

We define Hardy spaces $H^p(D'_\beta)$ on the non-smooth worm domain $D'_\beta=\{(z_1,z_2)\in\mathbb{C}^2:|Im z_1-\log |z_2|^2|<\frac{\pi}{2}, |\log |z_2|^2|<\beta-\frac{\pi}{2}\}$ and we prove a series of related results such as the…

Let $M$ be the Hardy-Littlewood maximal function and $b$ be a locally integrable function. Denote by $M_b$ and $[b,M]$ the maximal commutator and the (nonlinear) commutator of $M$ with $b$. In this paper, the author consider the boundedness…

The analysis of Morrey spaces, generalized Morrey spaces and $BMO_\phi$ spaces related to the Dunkl operators on $\mathbb{R}$ are covered in this paper. We prove the boundedness of the Hardy-Littlewood maximal operators, Bessel-Riesz…

We consider the non-linear thermoelastic plate equation in rectangular domains $\Omega$. More precisely, $\Omega$ is considered to be given as the Cartesian product of whole or half spaces and a cube. First the linearized equation is…

This paper describes the known results on the projection from the most general holomorphic spaces $A^p_\omega$, which depend on a functional parameter $\omega$ and are over the unit disc, upper half-plane and the finite complex plane, to…

Let H be the space of quaternions, with its standard hypercomplex structure. Let R(D) be the module of regular functions on D. For every unitary vector p in S^2, R(D) contains the space of holomorphic functions w.r.t. the complex structure…

We introduce a generalization of the Bourgain-Rosenthal-Schechtman $R_{\omega}^p$ space: Let $Y$ be a Haar system Hardy space, i.e., a separable rearrangement-invariant function space on the unit interval or an associated Hardy space…

We characterize the boundedness properties on the spaces $L^p(\mathbb{H}^2)$ of the maximal operator $M_\mathcal{B}$ where $\mathcal{B}$ is an arbitrary family of hyperbolic triangles stable by isometries.

We determine the spectrum of the Voltterra-type integral operators $V_g$ on the growth type Fock--Sobolev spaces $\mathcal{F}_{\psi_m}^\infty$. We also characterized the bounded and compact spectral properties of the operators in terms of…

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…

We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over…

In this article we investigate $L^p$ boundedness of the spherical maximal operator $\mathfrak{m}^\alpha$ of (complex) order $\alpha$ on the $n$-dimensional hyperbolic space $\mathbb{H}^n$, which was introduced and studied by El Kohen. We…

Let S be the semidirect product of R^d and R^+ endowed with the Riemannian symmetric space metric and the right Haar measure: this is a Lie group of exponential growth. In this paper we define an Hardy space H^1 and a BMO space in this…

A nonlinear superposition operator $T_g$ related to a Borel measurable function $g:\ {\mathbb C}\to {\mathbb C}$ is defined via $T_g(f):=g\circ f$ for any complex-valued function $f$ on ${\mathbb R^n}$. This article is devoted to…

We study the behaviour on rearrangement-invariant spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the fractional version), the Hilbert and Stieltjes transforms, and the…

We define the notion of a thick open set $\Omega$ in a Euclidean space and show that a local Hardy-Littlewood inequality holds in $L^p(\Omega)$, $p \in (1, \infty]$. We then establish pointwise and $L^p(\Omega)$ convergence for families of…

We extend the concept of a finite dimensional {\it holomorphic homogeneous regular} (HHR) domain and some of its properties to the infinite dimensional setting. In particular, we show that infinite dimensional HHR domains are domains of…

It is studied that pointwise estimates and continuities on Hardy spaces of pseudo-differential operators (PDOs for short) with the symbol in general H\"{o}rmander's classes. We get weighted weak-type $(1,1)$ estimate, weighted normal…

A Haar system Hardy space is the completion of the linear span of the Haar system $(h_I)_I$, either under a rearrangement-invariant norm $\|\cdot \|$ or under the associated square function norm \begin{equation*} \Bigl\| \sum_Ia_Ih_I…

In this paper we study optimal estimates for two functionals involving the anisotropic $p$-torsional rigidity $T_p(\Omega)$, $1<p<+\infty$. More precisely, we study $\Phi(\Omega)=\frac{T_p(\Omega)}{|\Omega|M(\Omega)}$ and…