M. Lacey

activity

19992005

most citedVariations on the Theme of Journe's Lemma

19 citations · 31 across the 6 of their papers we have counts for

collaborators

Showing 2000Show all

2 papers · 1 filter

math.CA2000

On the Hilbert transform and lacunary directions in the plane

Michael T. Lacey

Let $H_{k}$ be the one dimensional Hilbert transform computed in the direction $(1, 2^{k})$ in the plane. We show that the maximal operator $sup_{k} ∣ H_{k} f ∣$ maps $L^{p}$ of the plane into…

math.CA2000

The bilinear maximal functions map into L^p for 2/3 < p <= 1

Michael T. Lacey

The bilinear maximal operator defined below maps $L^{p} \times L^{q}$ into $L^{r}$ provided $1<p,q<\zI$, $1/ p + 1/ q = 1/ r$ and $2/3 < r \leq 1$ . $$ Mfg(x)=\sup_{t>0}\frac1{2t}\int_{-t}^t\abs{f(x+y…