Related papers: Real-variable characterizations of Bergman spaces
In this paper, we present maximal and area integral characterizations of Bergman spaces in the unit ball of $\mathbb{C}^n.$ The characterizations are in terms of maximal functions and area integral functions on Bergman balls involving the…
We prove vector-valued boundedness of (suitable) Calderon-Zygmund operators and of the (truncated) Hardy-Littlewood maximal function on a connected locally doubling metric measure space.
In this paper, the main aim is to consider the boundedness of commutators of multilinear Calder\'{o}n-Zygmund operators with Lipschitz functions in the context of the variable exponent Lebesgue spaces. Furthermore, the variable versions of…
In this paper, we give a complete real-variable theory of local variable Hardy spaces. First, we present various real-variable characterizations in terms of several local maximal functions. Next, the new atomic and the finite atomic…
It is well-known that several classical results about Calder\'{o}n-Zygmund singular integral operators can be extended to \(X\)-valued functions if and only if the Banach space \(X\) has the UMD property. The dependence of the norm of an…
In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators…
We characterize functions of a Bergman space on a square by their values and derivatives on the diagonals. This problem is connected with the reachable space of the one-dimensional heat equation on a finite interval with boundary…
On a two dimensional Stein space with isolated, normal singularities, smooth finite type boundary, and locally algebraic Bergman kernel, we establish an estimate on the type of the boundary in terms of the local algebraic degree of the…
In this paper, we introduce new spaces of holomorphic functions on the unit ball $\mathbb{B}_{n}$ of $\mathbb{C}^{n}$ generalizing the classical Bergman spaces. The main results include the properties of some operators and integrals…
We make use of the Bergman kernel function to study quadrature domains for square-integrable holomorphic functions of several variables. Emphasis is given to generalizing biholomorphic mapping properties of planar quadrature domains to the…
We proceed with studying the q-analogues of Cartan domains introduced in q-alg/9703005 and turn to the case of a ball in the space of complex matrices. An explicit expression for a positive $U_q\frak{su}_{nm}$-invariant integral (see…
This article is a continuation of our work on generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. In this article, we establish the boundedness of pseudo-differential, trace, and…
We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of…
This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.
Let $\Gamma\subset \mathrm{SU}((2,1),\mathbb{C})$ be a torsion-free cocompact subgroup. Let $\mathbb{B}^{2}$ denote the $2$-dimensional complex ball endowed with the hyperbolic metric $\mu_{\mathrm{hyp}}$, and let…
Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, the authors introduce the weak Hardy-type space $WH_X({\mathbb R}^n)$, associated with $X$, via the radial maximal function. Assuming that the powered…
We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on…
Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a H\"ormander class of critical order, we investigate boundedness properties of strongly singular Calder\'on--Zygmund operators in the bilinear…
The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the $A_2$ theorem for Calder\'on-Zygmund operators in harmonic…
This paper establishes that multilinear Calder\'on--Zygmund operators and their maximal operators are bounded on Hardy spaces associated with ball quasi-Banach function spaces. Moreover, we also obtain the boundedness of multilinear…