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Pointwise estimate for the Hardy-Littlewood maximal operator on the orbits of contractive mappings
(Academic Press Inc Elsevier Science, 2012-11)
Let M n denote the Hardy-Littlewood maximal operator on the n-th iteration of a given iterated function system (IFS). We give sufficient conditions on the IFS in order to obtain a pointwise estimate for M n in terms of the ...
On the sharp upper bound related to the weak Muckenhoupt–Wheeden conjecture
(Mathematical Sciences Publishers, 2020-09-12)
We construct an example showing that the upper bound [w]A1log(e+[w]A1) for the L1(w)→L1,∞(w) norm of the Hilbert transform cannot be improved in general.
The Calderón operator and the Stieltjes transform on variable Lebesgue spaces with weights
(Universidad de Barcelona, 2019-11)
We characterize the weights for the Stieltjes transform and the Calder´on operator to be bounded on the weighted variable Lebesgue spaces $L_w^{p(cdot)}(0,infty)$, assuming that the exponent function $pp$ is log-H"older ...
Hörmander conditions for vector-valued kernels of singular integrals and their commutators
(Unión Matemática Argentina, 2019-06)
We study Coifman type estimates and weighted norm inequalities for singular integral operators and their commutators, given by the convolution with a vector-valued kernel. We define a weaker Hörmander type condition ...
Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
(Michigan Mathematical Journal, 2019-09)
We study mixed weak type inequalities for the commutator [b,T], where b is a BMO function and T is a Calderón-Zygmund operator. Our technique involves the classical Calderón–Zygmund decomposition, which allows us to give ...
A1 bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden
(International Press Boston, 2009-12)
We obtain an Lp(ω) bound for Calderón-Zygmund operators T when w∈ A1. This bound is sharp both with respect to ||ω||A1 and with respect to p. As a result, we get a new L1,∞°(ω) estimate for T related to a problem of ...
Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
(Birkhäuser Publishing, 2009)
Improvements on Sawyer type estimates for generalized maximal functions
(Wiley VCH Verlag, 2020)
End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications
(American Mathematical Society, 2020-10-20)
In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. ...
The structure of increasing weights on the real line
(University of Houston, 2008-12)
We examine the structure of a variety of related weight classes on the real line and the positive real axis: doubling measures, Ap weights, the Bp weights of Ari˜no and Muckenhoupt, and 2 Young functions. We give a number ...