Related papers: Mixed weak type estimates: Examples and counterexa…
We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional integral operators. We consider a kind of weak-type inequality that was first studied by…
We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calder\'on-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating…
We study mixed weak estimates of Sawyer type for maximal operators associated to the family of Young functions $\Phi(t)=t^r(1+\log^+t)^{\delta}$, where $r\geq 1$ and $\delta\geq 0$. More precisely, if $u$ and $v^r$ are $A_1$ weights, and…
We prove mixed weak estimates of Sawyer type for fractional operators. More precisely, let $\mathcal{T}$ be either the maximal fractional function $M_\gamma$ or the fractional integral operator $I_\gamma$, $0<\gamma<n$, $1\leq p<n/\gamma$…
In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main result of the…
In this paper we provide mixed weak type inequalities generalizing previous results in an earlier work by Caldarelli and the second author and also in the spirit of earlier results by Lorente, Martell, P\'erez and Riveros. One of the main…
We prove mixed inequalities for the Hardy-Littlewood maximal function $M^{\rho,\sigma}$, where $\rho$ is a critical radius function and $\sigma\geq 0$. We also exhibit and prove an extension of Cruz-Uribe, Martell and P\'erez extrapolation…
We present a multi-variable extension of Rubio de Francia's restricted weak-type extrapolation theory that does not involve Rubio de Francia's iteration algorithm; instead, we rely on the following Sawyer-type inequality for the weighted…
In this paper, we establish quantitative weak type estimates for operators that are dominated by (fractional) sparse operators in bilinear sense. Specifically, we derive bounds for both the restricted weak type $L^{p,1}\rightarrow…
We prove a weak-type estimate for a class of operators extending some of the almost orthogonality issues involved in the study of the bilinear Hilbert transform by Lacey and Thiele.
Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical…
Two proofs of a weighted weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for multilinear Calder\'on-Zygmund operators are given. The ideas are motivated by different proofs of the classical weak-type $(1,1)$ estimate for…
In this article, we investigate the weighted $m-$subharmonic functions. We shall give some properties of this class and consider its relation to the $m-$Cegrell classes. We also prove an integration theorem and an almost everywhere…
We study mixed weak type inequalities for the commutator $[b,T]$, where $b$ is a BMO function and $T$ is a Calder\'on-Zygmund operator. More precisely, we prove that for every $t>0$ \begin{equation*}%\label{tesis_teo2.2} uv(\{x\in\R^n:…
We present a new proof of the classical weak-type $(1,1)$ estimate for Calder\'on-Zygmund operators. This proof is inspired by ideas of Nazarov, Treil, and Volberg that address the non-doubling setting. An application to a weighted…
We characterize two weight inequalities for general positive dyadic operators. We consider both weak and strong type inequalities, and general (p,q) mapping properties. Special cases include Sawyers Fractional Integral operator results from…
Let $S_{\alpha}$ be the multilinear square function defined on the cone with aperture $\alpha \geq 1$. In this paper, we investigate several kinds of weighted norm inequalities for $S_{\alpha}$. We first obtain a sharp weighted estimate in…
In this paper we prove mixed inequalities for the maximal operator $M_\Phi$, for general Young functions $\Phi$ with certain additional properties, improving and generalizing some previous estimates for the Hardy-Littlewood maximal operator…
We prove the endpoint weak type estimate for square functions of Marcinkiewicz type with fractional integrals associated with non-isotropic dilations. This generalizes a result of C. Fefferman on functions of Marcinkiewicz type by…
In this note the weak type estimates for fractional integrals are studied. More precisely, we adapt the arguments of Domingo-Salazar, Lacey, and Rey to obtain improvements for the endpoint weak type estimates for regular fractional sparse…