Related papers: A Two-Weight Inequality for Essentially Well Local…

Let $\mu$ be a Radon measure on $R^d$, which may be non doubling. The only condition that $\mu$ must satisfy is $\mu(B(x,r))\leq C r^n$, for all $x,r$ and for some fixed $0<n\leq d$. Recently we introduced spaces of type $BMO(\mu)$ and…

We consider a uniformly elliptic operator $L_A$ in divergence form associated with an $(n+1)\times(n+1)$-matrix $A$ with real, merely bounded, and possibly non-symmetric coefficients. If $$\omega_A(r)=\sup_{x\in \mathbb{R}^{n+1}}…

We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund type spaces. Consequently, we obtain new characterizations for the compactness of such…

We establish optimal $C^s$ boundary regularity for the most general class of (linear and translation invariant) nonlocal elliptic operator of order $2s$. Namely, we consider L\'evy operators that are symmetric and its Fourier symbol…

The questions of dense definiteness and boundedness of composition operators in $L^2$-spaces are studied by means of inductive limits of operators. Methods based on projective systems of measure spaces and inductive limits of $L^2$-spaces…

Motivated by the testing condition for Radon-Brascamp-Lieb multilinear functionals established in arXiv:2201.12201, this paper is concerned with identifying local conditions on smooth maps $u(t)$ with values in the space of decomposable…

$L^p$ to $L^p_{\beta}$ boundedness theorems are proven for translation invariant averaging operators over hypersurfaces in Euclidean space. The operators can either be Radon transforms or averaging operators with multiparameter fractional…

We continue developing the theory of conical and vertical square functions on $R^{n}$, where $\mu$ is a power bounded measure, possibly non-doubling. We provide new boundedness criteria and construct various counterexamples. First, we prove…

We use the principle of almost orthogonality to give a new and simple proof that a sparse Lerner operator is bounded on a matrix- or operator-weighted space $L_W^{2}(\mu)$, where $\mu$ is a doubling measure on $\R^d$ if and only if the…

We give a domination condition implying good-$\lambda$ and exponential inequalities for couples of measurable functions. Those inequalities recover several classical and new estimations involving some operators in Harminic Analysis. Among…

We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…

It is shown that the algebra \(L^\infty(\mu)\) of all bounded measurable functions with respect to a finite measure \(\mu\) is localizing on the Hilbert space \(L^2(\mu)\) if and only if the measure \(\mu\) has an atom. Next, it is shown…

We present a general framework of localized operators, i.e., operators whose matrix coefficients with respect to the Gabor frame are concentrated on the diagonal. We show that localized operators are bounded between modulation spaces, and…

We establish new upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space by introducing weighted geometric means of the modulus of an operator and its adjoint. This approach yields a family of…

Let $({\mathcal X}, d, \mu)$ be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition and the non-atomic condition that $\mu(\{x\})=0$ for all $x\in{\mathcal X}$. In this paper,…

We prove new concentration estimates for random variables that are functionals of a Poisson measure defined on a general measure space. Our results are specifically adapted to geometric applications, and are based on a pervasive use of a…

In this paper we consider the symmetric Kolmogorov operator $L=\Delta +\frac{\nabla \mu}{\mu}\cdot \nabla$ on $L^2(\mathbb R^N,d\mu)$, where $\mu$ is the density of a probability measure on $\mathbb R^N$. Under general conditions on $\mu$…

In this work sufficient conditions on the order of the symbol are developed to ensure boundedness, compactness and r-nuclearity of pseudo-differential operators in $\hbar\mathbb{Z}^n$. In addition, these conditions allow us to obtain growth…

This study investigates conditions for the boundedness of Forelli-Rudin type operators on weighted Lebesgue spaces associated with tubular domains over the generalized light cone. We establish a complete characterization of the boundedness…

We prove that convolution with affine arclength measure on the curve parametrized by $h(t) := (t,t^2,...,t^n)$ is a bounded operator from $L^p(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$ for the full conjectured range of exponents, improving on a…