Now showing items 1-10 of 61
New estimates for the maximal singular integral [Article]
(Oxford University Press, 2010)
In this paper we pursue the study of the problem of controlling the maximal singular integral T∗ f by the singular integral T f. Here T is a smooth homogeneous Calder´on-Zygmund singular integral of convolution type. ...
Potential operators, maximal functions, and generalizations of A∞ [Article]
We derive weighted norm estimates which relate integral operators of potential type (fractional integrals) to corresponding maximal operators (fractional maximal operators). We also derive norm estimates for the maximal ...
Weighted norm inequalities for singular integral operators [Article]
(London Mathematical Society, 1994-04)
For a Calderón-Zygmund singular integral operator T, we show that the following weighted inequality holds Z Rn|T f(y)|p w(y)dy ≤ C Z Rn |f(y)| p M[p]+1w(y)dy, where Mk is the Hardy-Littlewood maximal operator M iterated ...
A remark on weighted inequalities for general maximal operators [Article]
(American Mathematical Society, 1993-12)
Let 1 < p < ∞, and let w, v be two non–negative functions. We give a sufficient condition on w, v for which the general maximal operator MB is bounded from Lp(v) into Lp(w). Our condition is stronger but closely related to ...
Estimates with A∞ weights for various singular integral operators [Article]
Si studia la limitazione di certe classi di integrale singolari sullo spazio Lp(w), w € A∞.
Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture [Article]
We prove two-weight norm inequalities for Calderón-Zygmund singular integrals that are sharp for the Hilbert transform and for the Riesz transforms. In addition, we give results for the dyadic square function and for ...
Lack of natural weighted estimates for some singular integral operators [Article]
(American Mathematical Society, 2005)
A new quantitative two weight theorem for the Hardy-Littlewood maximal operator [Article]
(American Mathematical Society, 2015-02)
A quantitative two weight theorem for the Hardy-Littlewood maximal operator is proved improving the known ones. As a consequence a new proof of the main results in [HP] and in [HPR12] is obtained which avoids the use of ...
The L(log L)e endpoint estimate for maximal singular integral operators [Article]
We prove in this paper the following estimate for the maximal operator T ∗ associated to the singular integral operator T: kT ∗ fkL 1,∞ (w) . 1 ǫ Z Rn | f(x)| ML(log L) ǫ (w)(x) dx, w ≥ 0, 0 < ǫ ≤ 1. This ...