## Preprints in Kakeya and Restriction problems

There are other pages on the web on Kakeya and Restriction; Ben Green, Alex Iosevich, and Izabella Laba all maintain one.  If you are new to this field and want to learn more, I can suggest starting with my Notices article surveying this field.  If you then want to learn more about the Kakeya problem, you could try the El Escorial proceedings survey with Nets Katz, or the Edinburgh lecture notes on the Kakeya problem; if you want to learn more about the restriction problem, I can offer my Park city notes on the Restriction problem.  You can also see my Math 254B home page for a more leisurely-paced introduction, but it is getting a little out of date. If you are more into the algebraic side of things, you can learn about the finite field analogues of these problems in this paper with Gerd Mockenhaupt.  If you like the arithmetic combinatorial side of things, you can start with this short paper with Nets, or my Math 254A home page.  If you are instead interested in the Bochner Riesz or local smoothing problems, you will have to go to my research papers, such as my second paper with Ana Vargas; I do not yet have a good survey of these problems (one should probably go look instead at the home pages of Izabella Laba or of the papers of Tom Wolff), although I mention these problems briefly in the Park city notes.

## Math 254B home page - Restriction theorems, Bochner-Riesz, Kakeya, etc. (1999)

### Papers, and projects close to completion

 Title With Status Download Proc. Amer. Math. Soc. 124 (1996), 2797-2805 Duke Math. J. 96 (1999), 363-376 dvi ps.Z Slides: dvi  ps.Z Indiana U. Math. J. 47 (1998), 1097-1124 dvi Slides: dvi  ps.Z A bilinear approach to the restriction and Kakeya conjectures Ana Vargas Luis Vega J. Amer. Math. Soc. 11 (1998), 967-1000 math.CA/9807163 Slides: dvi + Figures 12 Summary: dvi Trans. Amer. Math. Soc. 354 (2002), 1947-1959 dvi + Figure 1 ps.Z Slides: dvi + Figures 1234 A bilinear approach to cone multipliers I. Restriction estimates Ana Vargas GAFA 10 (2000), 185-215 dvi + Figures 12345 ps Summary: dvi A bilinear approach to cone multipliers II. Applications Ana Vargas GAFA10 (2000), 216-258 dvi + Figures 12345 ps An improved bound on the Minkowski dimension of Besicovitch sets in R^3 Annals of Math. 152 (2000),  383-446 math.CA/9903166 Slides: dvi + Figures 1234567 Math. Z. 238 (2001), 215-268 math.CA/9909066 Non-endpoint: dvi Informal: dvi Slides: dvi + Figures 1234567 Bounds on arithmetic projections, and applications to the Kakeya conjecture Nets Katz Math. Res. Letters 6 (1999), 625-630 math.CO/9906097 Slides: dvi + Figures 1234567 An x-ray transform estimate in R^n Izabella Laba Revista Mat. Iber. 17 (2001), 375-408 math.CA/9909032 Informal: dvi Some connections between the Falconer and Furstenburg conjectures Nets Katz New York J. Math. 7 (2001), 148-187 An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension Izabella Laba GAFA 11 (2001), 773-806 math.CA/0004015 Notices Amer. Math. Soc. 48 (2001) No 3, 294-303 Kakeya and restriction phenomena for finite fields Gerd Mockenhaupt Duke Math. J. 121 (2004), 35-74 math.CA/0204234 New bounds for Kakeya problems Nets Katz Journal d'Analyse de Jerusalem,  87 (2002), 231-263 math.CA/0102135 Slides + Figure 1234567 Recent progress on the Kakeya conjecture Nets Katz Publicacions Matematiques, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, U. Barcelona 2002, 161-180 math.CA/0010069 Bochner-Riesz summability for analytic functions on the  m-complex unit sphere and for cylindrically symmetric functions on R^{n-1} \times R Adam Sikora Comm. Anal. Geom. 12 (2004), 43-57 math.CA/0207225 A new bound for finite field Besicovitch sets in four dimensions Pacific J. Math 222 (2005), 337-363 math.CA/0204251 A sharp bilinear restriction estimate for paraboloids GAFA 13 (2003), 1359-1384 math.CA/0210084 Some recent progress on the Restriction conjecture Fourier analysis and convexity, 217-243, Birkhäuser Boston, Boston, MA, 2004. math.CA/0303136 Recent progress on the Restriction conjecture to appear, Park City proceedings math.CA/0311181 On the Multilinear Restriction and Kakeya conjectures Jon Bennett Tony Carbery Acta Math.  196 (2006) 261—302 math.CA/0509262 The Kakeya set and maximal conjectures for algebraic varieties over finite fields Jordan Ellenberg Richard Oberlin to appear, Mathematika arXiv:0903.1879 discussion

Some further papers related to Kakeya and restriction problems can be found on my PDE preprint page.
Some further papers dealing with more general aspects of harmonic analysis can be found here.

### Miscellaneous

Back to my preprints page.