110 citations · 202 across the 6 of their papers we have counts for
6 papers
Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals
Tuomas P. Hytönen, Michael T. Lacey, Carlos Pérez
Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler t…
On the Convergence of Lacunary Walsh-Fourier Series
Yen Do, Michael T. Lacey
We study the Walsh-Fourier series of S_{n_j}f, along a lacunary subsequence of integers {n_j}. Under a suitable integrability condition, we show that the sequence converges to f a.…
Benedick's theorem for the Heisenberg group
E. K. Narayanan, P. K. Ratnakumar
If is a compactly supported function on the Heisenberg group and the group Fourier transform is a finite rank operator for all then is the zero function.
A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure
M. T. Lacey, E. T. Sawyer, I. Uriarte-Tuero
We characterize two-weight inequalities for certain maximal truncations of the Hilbert transform in terms of testing conditions on simpler functions. For 1<p<2 and two positive Bor…
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this paper has been withdrawn.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.