Related papers: Equivalent Characterizations for Boundedness of Ma…

In this paper, we study the $L^{p}$ boundedness and $L^{p}(w)$ boundedness ($1<p<\infty$ and $w$ a Muckenhoupt $A_{p}$ weight) of fractional maximal singular integral operators $T_{\Omega,\alpha}^{\#}$ with homogeneous convolution kernel…

For a limited range of indices $p$, we obtain $L^p(\mathbb{R}^n)$ boundedness for singular integral operators whose kernels satisfy a condition weaker than the typical H\"ormander smoothness estimate. These operators are assumed to be…

We establish precise regularity conditions for $L_p$-boundedness of Fourier multipliers in the group algebra of $SL_n(\mathbf{R})$. Our main result is inspired by H\"ormander-Mikhlin criterion from classical harmonic analysis, although it…

Let $(X,d,\mu)$ be a metric space with doubling measure and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ whose heat kernel satisfies the Gaussian upper bound. We assume that there exists an $L$-harmonic function $h$ such that the…

In this paper we study ``Bergman-type'' singular integral operators on Ahlfors regular metric spaces. The main result of the paper demonstrates that if a singular integral operator on a Ahlfors regular metric space satisfies an additional…

The purpose of this paper is to describe the smooth homogeneous Calderon-Zygmund operators for which the maximal singular integral T*f may be controlled by the singular integral Tf. We consider two types of control. The first is the L2…

In this paper, we describe families of those bounded linear operators on a separable Hilbert space that are simultaneously unitarily equivalent to integral operators on $L_2(R)$ with bounded and arbitrarily smooth Carleman kernels. The main…

Let $(X,d,\mu)$ be a metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions, which is called non-homogeneous metric measure space. In this paper, via a sharp maximal operator, the…

We find optimal conditions on $m$-linear Fourier multipliers to give rise to bounded operators from a product of Hardy spaces $H^{p_j}$, $0<p_j\le 1$, to Lebesgue spaces $L^p$. The conditions we obtain are necessary and sufficient for…

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…

In this paper we pursue the study of the problem of controlling the maximal singular integral $T^{*}f$ by the singular integral $Tf$. Here $T$ is a smooth homogeneous Calder\'on-Zygmund singular integral of convolution type. We consider two…

In this note we provide a quick proof that maximal truncations of oscillatory singular integrals are bounded from $L^1(\mathbb{R})$ to $L^{1,\infty}(\mathbb{R})$. The methods we use are entirely elementary, and rely only on pigeonholing and…

We provide a characterization of $\mathrm{BMO}$ in terms of endpoint boundedness of commutators of singular integrals. In particular, in one dimension, we show that $\|b\|_{\mathrm{BMO}}\eqsim B$, where $B$ is the best constant in the…

Let $\mu$ be a non-negative Radon measure on ${\mathbb R}^d$ which only satisfies the polynomial growth condition. Let ${\mathcal Y}$ be a Banach space and $H^1(\mu)$ the Hardy space of Tolsa. In this paper, the authors prove that a linear…

In this paper, we prove that the oscillation operator, variation operator and maximal differential transform associated with the approximate identities are bounded from ${\rm BMO}({\mathbb R}^n)$ to its subspace ${\rm BLO}({\mathbb R}^n)$.

The famous $T1$ theorem for classical Calder\'on-Zygmund operators is a characterisation for their boundedness in $L^{2}$. In the bi-parameter case, on the other hand, the current $T1$ theorem is merely a collection of sufficient…

In this paper we introduce Calder\'on-Zygmund theory for singular stochastic integrals with operator-valued kernel. In particular, we prove $L^p$-extrapolation results under a H\"ormander condition on the kernel. Sparse domination and sharp…

The purpose of this paper is to study the $L^p$ boundedness of operators of the form \[ f\mapsto \psi(x) \int f(\gamma_t(x))K(t)\: dt, \] where $\gamma_t(x)$ is a $C^\infty$ function defined on a neighborhood of the origin in $(t,x)\in…

This paper investigates the boundedness of bilinear pseudo-differential operators with symbols in the H\"{o}rmander class $BS_{\varrho,\delta}^m(\mathbb{R}^n)$ in the previously unexplored regime $0 \leq \varrho < \delta < 1$. We establish…

We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy-Sobolev spaces $\dot{H}^{1,p}(\mathbb{R}^d)$ when $1/p < 1+1/d$. This range of exponents is sharp. As a by-product of the…