19 citations · 31 across the 6 of their papers we have counts for
11 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…
Carleson's Theorem: Proof, Complements, Variations
Michael Lacey
Carleson's Theorem asserts the pointwise convergence of Fourier series of square integrable functions. We give a complete proof, following joint work of the author and C. Thiele. O…
Issues related to Rubio de Francia's Littlewood--Paley Inequality: A Survey
Michael T Lacey
Rubio de Francia's Littlewood Paley inequality is an extension of the classical Littlewood Paley inequality to one that holds for a decomposition of frequency space into arbitrary…