19 citations · 29 across the 4 of their papers we have counts for
6 papers · 1 filter
Commutators with Reisz Potentials in One and Several Parameters
Michael T Lacey
Let be the operator of pointwise multiplication by , that is . Set . The Reisz potentials are the operators $$ R_αf(x)=\int f(x-…
Variations on the Theme of Journe's Lemma
Carlos Cabrelli, Michael Lacey, Ursula Molter +1
Journe's Lemma is a critical component of many questions related to the product theory of S.-Y. Chang and R. Fefferman. This article presents several different variants of…
Rubio de Francia Littlewood Paley Inequalities and Directional Maximal Functions
Grigor Karagulyan, Michael T Lacey
In , define a maximal function in the directions $v\in \directions\subset\{x \mid \abs x=1\}$ by $$ M^\directions f(x)=\sup_{v\in\directions} \sup_{\zve} \int_{-\ze}^\ze \abs{…
An Estimate of the Maximal Operators Associated with Generalized Lacunary Sets
Grigor Karagulyan, Michael T Lacey
Let be any set of directions (unit vectors) on the plane. In this paper we study maximal operator of the one dimensional maximal function computed in the directions of We a…
Maximal Theorems for the Directional Hilbert Transform on the Plane
Michael T Lacey, Xiaochun Li
For a Schwartz function on the plane and a non-zero $v\in\ZR^2$ define the Hilbert transform of in the direction to be $$ H_vf(x)=\text{p.v.}\int_\ZR f(x-vy) \frac{dy}y…
On the Hilbert Transform and $C^{1+\ze}$ Families of Lines
Michael T Lacey, Xiaochun Li
this paper has been withdrawn. A crucial estimate on a Lipschitz variant of the Kakeya maximal function has an incomplete proof.