Related papers: A Christ-Fefferman type approach to the one sided …
The purpose of this note is to prove that the strong Christ-Goldberg maximal function is bounded. This is a matrix weighted maximal operator appearing in the theory of matrix weighted norm inequalities. Related to this we record the Rubio…
We provide a Fefferman-Stein type weighted inequality for maximally modulated Calder\'on-Zygmund operators that satisfy \textit{a priori} weak type unweighted estimates. This inequality corresponds to a maximally modulated version of a…
Following the ideas of Andrei Lerner in [ A pointwise estimate for the local sharp maximal function with applications to singular integrals" Bull. London Math. Soc. 42 (2010) 843856], we obtain another decomposition of an arbitrary…
In this paper we provide some quantitative one-sided estimates that recover the dependences in the classical setting. Among them we provide estimates for the one-sided maximal function in Lorentz spaces and we show that the conjugation…
In this paper we obtain the sharp quantitative matrix weighted weak type bounds for the Christ--Goldberg maximal operator $M_{W,p}$ in the case $1<p<2$, improving a recent result by Cruz-Uribe and Sweeting. Also, in the scalar setting, we…
The Fefferman-Stein type inequality for strong maximal operator is verified with compositions of some maximal operators in the heigher dimensions. An elementary proof of the endpoint estimate for the strong maximal operator is also given.
We derive criteria governing two-weight estimates for multilinear fractional integrals and appropriate maximal functions. The two and one weight problems for multi(sub)linear strong fractional maximal operators are also studied; in…
We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the…
We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture, thus strengthening the counterexamples built by Reguera--Thiele. We show a certain logarithmic blow-up for…
We prove some Sawyer-type characterizations for multilinear fractional maximal function for the upper triangle case. We also provide some two-weight norm estimates for this operator. As one of the main tools, we use an extension of the…
We prove two-weight norm inequalities for parabolic fractional maximal functions using parabolic Muckenhoupt weights. In particular, we prove a two-weight, weak-type estimate and Fefferman-Stein type inequalities for the centered parabolic…
The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal…
We study classical weighted $L^p\to L^q$ inequalities for the fractional maximal operators on $\R^d$, proved originally by Muckenhoupt and Wheeden in the 70's. We establish a slightly stronger version of this inequality with the use of a…
Quantitative formulations of Fefferman's counterexample for the ball multiplier are naturally linked to square function and vector-valued estimates for directional singular integrals. The latter are usually referred to as Meyer-type lemmas…
In this article, we present weighted norm inequality for a fractional one-sided minimal function. We prove weighted weak and strong type norm inequalities for the one-sided minimal function on $\mathbb{R}.$ We construct two weight classes…
We give again (see also arXiv:1112.0676) a proof of weighted estimate of any Calder\'on-Zygmund operator. This is under a universal sharp sufficient condition that is weaker than the so-called bump condition. Bump conjecture was recently…
The paper is devoted to two-weight estimates for the fractional maximal operators $\mathcal{M}^\alpha$ on general probability spaces equipped with a tree-like structure. For given $1<p\leq q<\infty$, we study the sharp universal upper bound…
We provide some new estimates for Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to weighted spaces. Using a type of symmetrization principle, introduced for the dyadic maximal…
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…
In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain weighted weak and…