Related papers: Maximal polynomial modulations of singular integra…
Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms…
We give a new formulation of the $T1$ theorem for compactness of Calder\'on-Zygmund singular integral operators. In particular, we prove that a Calder\'on-Zygmund operator $T$ is compact on $L^2(\mathbb{R}^n)$ if and only if $T1,T^*1\in…
We prove the $L^p$ boundedness of a maximal operator associated with a dyadic frequency decomposition of a Fourier multiplier, under a weak regularity assumption.
We prove $L^p$ bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our bounds improve upon those obtained by I. {\L}aba and M. Pramanik and in some cases are sharp up to the endpoint. A…
The purpose of this article is to extend the uniqueness results for the two dimensional Calder\'on problem to unbounded potentials on general geometric settings. We prove that the Cauchy data sets for Schr\"odinger equations uniquely…
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…
We consider the higher order Schr\"odinger operator $H=(-\Delta)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2m$, $m\in \mathbb N$. We adapt our recent results for $m>1$ to show that the wave operators are bounded on…
We use Oberlin, Nazarov, and Thiele's Multi-Frequency Calder\'{o}n-Zygmund decomposition to lower estimates on maximal multipliers in $L^p$. We also improve on classical multiplier results of Coifman, Rubio de Francia, and Semmes.
We study the boundedness problem for maximal operators $\mathbb{M}$ associated to averages along families of finite type curves in the plane, defined by $$\mathbb{M}f(x) \, := \, \sup_{1 \leq t \leq 2} \left|\int_{\mathbb{C}} f(x-ty) \,…
Given $1\leq q<p<\infty$ quantitative weighted L^p estimates, in terms of Aq weights, for vector valued maximal functions, Calder\'on-Zygmund operators, commutators and maximal rough singular integrals are obtained. The results for singular…
In this paper we adapt the technique developed in [17] to show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type square functions, multipliers of Laplace or…
We study the maximal operator on the variable exponent H\"older spaces in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annular decay property. Let us stress that there are no…
We present an intrinsically defined algebra of operators containing the right and left invariant Calder\'on-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on L^p (1<p<\infty). This algebra…
In this paper, we consider the degenerate and singular oscillatory integral operator with a singular kernel which is not a Calder\'{o}n-Zygmund kernel and satisfies suitable size and derivative conditions related to a real parameter $\mu$.…
In this paper, we study the $L^{p}$-improving property for the maximal operators along a large class of curves of finite type in the plane with dilation set $E \subset [1,2]$. The $L^{p}$-improving region depends on the order of finite type…
The purpose of this paper is to prove optimal estimates for solutions of the Kohn-Laplacian for certain classes of model domains in several complex variables. This will be achieved by applying a type of singular integral operator whose…
The properties of the maximal operator of the $(C,\alpha)$-means ($\alpha=(\alpha_1,\ldots,\alpha_d)$) of the multi-dimensional Walsh-Kaczmarz-Fourier series are discussed, where the set of indices is inside a cone-like set. We prove that…
Extending the methods developed in the author's previous paper and using adapted coordinate systems in two variables, an L^p boundedness theorem is proven for maximal operators over hypersurfaces in R^3 when p > 2. When the best possible p…
This paper investigates the $L^p$-bounds of wave operators for higher-order Schr\"odinger operators $H = (-\Delta)^m + V$ on $\mathbb{R}^n$, with $m \ge 2$ and real-valued decaying potentials $V$. Our main objective is to establish the…
In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y),…