Related papers: A Fefferman-Stein inequality for the Carleson oper…
Our aim in this article is to study the weighted boundedness of the centered Hardy-Littlewood maximal operator in Harmonic $NA$ groups. Following Ombrosi et al. \cite{ORR}, we define a suitable notion of $A_p$ weights, and for such weights,…
For a general dyadic grid, we give a Calder\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of…
It is known that that the endpoint mixed norm estimate $|| \, ||Tf(x,y)||_{L_{x}^{p}}||_{L_{y}^{\infty}} \lesssim || \, ||f(x,y)||_{L_{x}^{p}}||_{L_{y}^{\infty}}$ in general does not hold for Calder\'on-Zygmund operator $T$. In this…
In this paper weighted endpoint estimates for the Hardy-Littlewood maximal function on {the infinite rooted} $k$-ary tree are provided. Motivated by Naor and Tao the following Fefferman-Stein estimate \[ w\left(\left\{ x\in…
We consider L^p two weight inequalities for maximal truncations of dyadic Calderon-Zygmund operators. In the case of one weight being doubling, a characterization is given, and for the general case, sufficient conditions are given,…
We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to $\mathbb{Z}_2^n$ (also negative values of the multiplicity function are…
We prove a bilinear Carleson embedding theorem with matrix weight and scalar measure. In the scalar case, this becomes exactly the well known weighted bilinear Carleson embedding theorem. Although only allowing scalar Carleson measures, it…
We develop a technique of proving standard estimates in the setting of Laguerre function expansions of convolution type, which works for all admissible type multi-indices $\alpha$ in this context. This generalizes a simpler method existing…
In this expository article we collect and discuss some recent results on different consequences of a Sharp Reverse H\"older Inequality for $A_{\infty}$ weights. For two given operators $T$ and $S$, we study $L^p(w)$ bounds of…
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 improve on several weighted inequalities of recent interest by replacing a part of the A_p bounds by weaker A_\infty estimates involving Wilson's A_\infty constant \[ [w]_{A_\infty}':=\sup_Q\frac{1}{w(Q)}\int_Q M(w\chi_Q). \] In…
Stein and Wainger proved the $L^p$ bounds of the polynomial Carleson operator for all integer-power polynomials without linear term. In the present paper, we partially generalise this result to all fractional monomials in dimension one.…
We give an overview of the generalized Calder\'on-Zygmund theory for "non-integral" singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted…
For $1<p<\infty$ and $M$ the centered Hardy-Littlewood maximal operator on $\mathbb{R}$, we consider whether there is some $\varepsilon=\varepsilon(p)>0$ such that $\|Mf\|_p\ge (1+\varepsilon)||f||_p$. We prove this for $1<p<2$. For $2\le…
Shifted variants of (dyadic) Hardy-Littlewood maximal function and Stein's square function have played a significant role in the study of many important operators such as Calderon commutators, (bilinear) Hilbert transforms, multilinear…
We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\mathbb{Z}_2^d$. Noteworthy, we admit negative values of the…
Let $n\ge 2$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator ${\mathfrak M}{\alpha}$ of order $\alpha$, $0\le\alpha<n$, on the weighted Choquet-Lorentz space…
In this paper, we establish estimates for the oscillation seminorm for the so-called Carleson--Dunkl operator on weighted $L^p(\mathbb{R},w(x)|x|^{2\alpha+1}{\rm d}x)$ spaces with power weights $w(x)=|x|^\beta$. As a result, we obtain…
The paper concerns the magnetic Schr\"odinger operator on $R^n$. Under certain conditions, given in terms of the reverse H\"older inequality on the magnetic field and the electric potential, we prove some $L^p$ estimates on the Riesz…
In this article, we first improve the scalar maximal theorem for the Dunkl maximal operator by giving some precisions on the behavior of the constants of this theorem for a general reflection group. Next we complete the vector-valued…