Related papers: Calder\'on-Zygmund operators in the Bessel setting

We introduce a class of operators on abstract measure spaces, which unifies the Calder\'on-Zygmund operators on spaces of homogeneous type, the maximal functions and the martingale transforms. We prove that such operators can be dominated…

We study Hardy space $H^1_L(X)$ related to a self-adjoint operator $L$ defined on Euclidean domain $X \subseteq \mathbb{R}^d$. Under certain assumptions on the heat semigroup $\exp(-tL)$ we prove characterization of $H^1_L(X)$ by the Riesz…

Through the study of novel variants of the classical Littlewood-Paley-Stein $g$-functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on $\mathbb{R}^d$ satisfying regularity hypotheses adapted to…

In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calder\'on--Zygmund singular integral operator,…

We derive an integral representation for the Jacobi-Poisson kernel valid for all admissible type parameters $\alpha,\beta$ in the context of Jacobi expansions. This enables us to develop a technique for proving standard estimates in the…

In this paper we study the behavior of some harmonic analysis operators associated with the discrete Laplacian $\Delta_d$ in discrete Hardy spaces $\mathcal H^p(\mathbb Z)$. We prove that the maximal operator and the Littlewood-Paley $g$…

We provide a natural BMO-criterion for the $L_2$-boundedness of Calder\'on-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix,…

In this paper we commence the study of discrete harmonic analysis associated with Jacobi orthogonal polynomials of order $(\alpha,\beta)$. Particularly, we give the solution $W^{(\alpha,\beta)}_t$, $t\ge 0$, and some properties of the heat…

It is shown that multilinear Calder\'on-Zygmund operators are bounded on products of Hardy spaces.

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…

In this paper, we study the boundedness theory for maximal Calder\'on-Zygmund operators acting on noncommutative $L_p$-spaces. Our first result is a criterion for the weak type $(1,1)$ estimate of noncommutative maximal Calder\'on-Zygmund…

Let $L_\nu = -\partial_x^2-(\nu-1)x^{-1} \partial_x$ be the Bessel operator on the half-line $X_\nu = [0,\infty)$ with measure $x^{\nu-1} \,\mathrm{d} x$. In this work we study singular integral operators associated with the Laplacian…

In this paper we obtain quantitative weighted $L^p$-inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $L^p(w)$-operator norms in…

In this paper, we consider the characterizations of the Lipschitz spaces and homogeneous Lipschitz spaces associated to the biharmonic operator $\Delta^2.$ With this characterizations, we prove the boundedness of the Bessel potentials,…

In this paper, we introduce a class of singular integral operators which generalize Calder\'on-Zygmund operators to the more general case, where the set of singular points of the kernel need not to be the diagonal, but instead, it can be a…

We study multivariable spectral multipliers $F(L_1,L_2)$ acting on Cartesian product of ambient spaces of two self-adjoint operators $L_1$ and $L_2$. We prove that if $F$ satisfies H\"ormander type differentiability condition then the…

We prove that a large class of operators, which arise as the projections of martingale transforms of stochastic integrals with respect to Brownian motion, as well as other closely related operators, are in fact Calder\'on--Zygmund…

We prove that Calder\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on…

We prove a general sparse domination theorem in a space of homogeneous type, in which a vector-valued operator is controlled pointwise by a positive, local expression called a sparse operator. We use the structure of the operator to get…

Calder\'on-Zygmund decompositions of functions have been used to prove weak-type (1,1) boundedness of singular integral operators. In many examples, the decomposition is done with respect to a family of balls that corresponds to some family…