Related papers: Muckenhoupt-type weights and the intrinsic structu…

In the 1970s Muckenhoupt and Wheeden made several conjectures relating two weight norm inequalities for the Hardy-Littlewood maximal operator to such inequalities for singular integrals. Using techniques developed for the recent proof of…

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,…

We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into…

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…

In this paper, we consider the weighted Hardy space $\mathcal{H}^p(\omega)$ induced by an $A_1$ weight $\omega.$ We characterize the positive Borel measure $\mu$ such that the identical operator maps $\mathcal{H}^p(\omega)$ into $L^q(d\mu)$…

We show that Petermichl's dyadic operator $\mathcal{P}$ (S. Petermichl (2000), Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol) is a Calder\'{o}n-Zygmund type operator on an adequate metric normal space of…

Let $\mathcal{M}(\mathbb{R}^n)$ be the class of bounded away from one and infinity functions $p:\mathbb{R}^n\to[1,\infty]$ such that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space…

Let $L$ be a one-to-one operator of type $\omega$ in $L^2(\mathbb{R}^n)$, with $\omega\in[0,\,\pi/2)$, which has a bounded holomorphic functional calculus and satisfies the Davies-Gaffney estimates. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$…

Assuming the bilinear reverse Holder's condition, we character weighted inequalities for the bilinear maximal operator on filtered measure spaces. We also obtain Hytonen-Perez type weighted estimates for the bilinear maximal operator. Our…

In this note we prove a multilinear version of the reverse H\"older inequality in the theory of Muckenhoupt $A_p$ weights. We give two applications of this inequality to the study of multilinear weighted norm inequalities. First, we prove a…

In this article we study a special class of non-doubling metric measure spaces for which there is a significant difference between the incidence of weak and restricted weak type $(p,p)$ inequalities for the centered and non-centered…

We characterize the compactness of commutators in the Bloom setting. Namely, for a suitably non-degenerate Calder\'on--Zygmund operator $T$, and a pair of weights $ \sigma , \omega \in A_p$, the commutator $ [T, b]$ is compact from $ L ^{p}…

Let $L_1$ be a nonnegative self-adjoint operator in $L^2({\mathbb R}^n)$ satisfying the Davies-Gaffney estimates and $L_2$ a second order divergence form elliptic operator with complex bounded measurable coefficients. A typical example of…

We study new weighted estimates for the 2-fold product of Hardy-Littlewood maximal operators defined by $M^{\otimes}(f,g):= MfMg$. This operator appears very naturally in the theory of bilinear operators such as the bilinear…

This paper establishes Carleson embeddings of M{\"u}ntz spaces $M^q_{\Lambda}$ into weighted Lebesgue spaces $L^p(\mathrm{d}\mu)$, where $\mu$ is a Borel regular measure on $[0,1]$ satisfying $\mu([1-\varepsilon])\lesssim…

Let $A^p_\omega$ denote the Bergman space in the unit disc induced by a radial weight~$\omega$ with the doubling property $\int_{r}^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$. The positive Borel measures such that the…

We show that the norm of the vector of Riesz transforms as operator in the weighted Lebesgue space L^2(w) is bounded by a constant multiple of the first power of the Poisson-A_2 characteristic of w. The bound is free of dimension. Our…

In this paper, we will study the boundedness of intrinsic square functions on the weighted Hardy spaces $H^p(w)$ for $0<p<1$, where $w$ is a Muckenhoupt's weight function. We will also give some intrinsic square function characterizations…

This paper develops the function and operator theory of Hardy--Carleson--type analytic tent spaces $AT_q^\infty(\omega)$ induced by radial weights $\omega$ satisfying a two-sided doubling condition. We first characterize the positive Borel…

Given a space of homogeneous type $(X,\mu,d)$, we prove strong-type weighted norm inequalities for the Hardy-Littlewood maximal operator over the variable exponent Lebesgue spaces $L^\pp$. We prove that the variable Muckenhoupt condition…