# Publications: Michael T. Lacey

Most of the research below was supported by the National Science Foundation. Research support has also been received from the Salem Prize, Guggenheim Foundation, the Fulbright Foundation, the Simons Foundation and several other mathematics research institutes.

[

]

## All the arxiv papers and the Non-arxiv papers are below.

1. S. Hofmann (with  P. Auscher, , J. Lewis,  A. McIntosh and P. Tchamitchian) La solution des conjectures de Kato C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 7, 601--606. dvi file. This paper surveys the results of the next two

Read Carlos Kenig's elegant review of the solution of the Kato square root problem, as it appears in MathSci.

2. S. Hofmann (with  P. Auscher,,  A. McIntosh and P. Tchamitchian) The solution of the Kato Square Root Problem for Second Order Elliptic Operators on $\RR^n$ Annal of Math 1566 (2002) 633-654.
3. A. McIntosh (with  S. Hofmann and )  The Solution of the Kato Problem in the case of Gaussian Heat Kernel Bounds (Annals of Math. 156 (2002) 623--631.)
4. (with C. Thieleps file and pdf file A complete, eight page proof of Carleson's theorem asserting the pointwise   convergence of Fourier series of square integrable functions
5. postscript. On the bilinear Hilbert transform.  Doc. Math. {\bf 1998}, Extra Vol. II, 647--656 (electronic);   pdf
6. (with R. Jones and M. Wierdl) Integer sequences with big gaps and the pointwise ergodic theorem. Ergodic Theory Dynam. Systems 19 (1999), no. 5, 1295--1308.
7. C. Thiele (with) On the Calderon Conjectures for the bilinear Hilbert Transform . Proc. Nat. Acad. Sci 95 (1998) 4828-4830.
8. C. Thiele (with ) Lp bounds for the bilinear Hilbert transform Annals Math 146 (1997) 693-724.
9. C. Thiele (with ) Lp bounds for the bilinear Hilbert transform Proc. Nat. Acad. Sci. USA 94 33-35.
10. The bilinear Hilbert transform is locally finite  Rev. Math. Iberoamericana 13 (1998) 411---469.
11.  On Bilinear Littlewood Paley Square Functions. Publicacions Mat. 40 (1996) 387--396.
12. The return time theorem fails on infinite measure preserving systems. Ann. Inst. Henri Poincare 33 (1997) 491---495.
13. On a Lemma of Bourgain Illinois J. Math. 41 (1997) 231---236.
14. Spectral criteria, SLLNs and a.\thinspace s.\ convergence of series of stationary variables (with C. Houdré) Ann. Probab. 24 (1996) 838---856.
15. Ergodic averages on circles To appear in J. D'Analyse 67 (1995) 199---206.
16. A sharp estimate of the $L^p$ norm of $u$ times the gradient of $v$. J. Math. Analysis Appl. 205 (1997) 554---559.
17. Bourgain's Entropy Criteria Proceedings of Ergodic Theory Conference, Columbus Ohio, July 1993.
18. Transferring the! Carleson--Hunt Theorem Proceedings of conference, Columbia Missouri, July 1994.
19. Random Ergodic Theorems with universally representative sequences. (with K. Petersen, D. Rudolph, M. Wierdl) Ann. Instit. H. Poincare (Probab. Statist.) 30 (1994) 353---395.
20. Weak convergence in dynamical systems to self--similar processes with spectral representation. Trans. Amer. Math. Soc. 328(1991) 767---778.
21. Weak convergence to self--affine processes in dynamical systems. In:New directions in times series analysis, part II. IMA volumes in applied mathematics and its applications, Vol. 46, Springer.
22. On central limit theorems, modulus of continuity and Diophantine type for irrational rotations. J. D'Analyse 61 (1993) 47---59.
23. Weak convergence in dynamical systems to self-similar processes with time average representation. In: Chaos expansions, multiple Wiener--Ito integrals and their applications. CRC Press, 1994. 163---177.
24. On almost sure non--central limit theorems. J. Theor. Probab. 4 (1991) 767---781.
25. Limit laws for local times of a Brownian sheet. Probab. Th. Rel. Fields 86 (1990) 63---85.
26. Large deviations for maximum local time of stable Levy processes. Ann. Probab. 18 (1990) 1669---1675
27. A note on the almost sure central limit theorem.  (with W. Philipp) Statist. Probab. Letters 9 (1990) 201---205.
28. A remark on the multiparameter law of the iterated logarithm. Stoch. Proc. Appl! . 32 (1989) 355---367.
29. Laws of the iterated logarithm for partial sum processes indexed by functions.J. Theor. Probab. 2 (1989) 377---398.
30. Laws of the iterated logarithm for the empirical characteristic function. Ann. Probab. 17 (1989) 292---300.