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Publications

John B. Garnett

Books:

1. J. Garnett, Analytic Capacity and Measure. Lecture Notes in Mathematics, Springer-Verlag. 297, 1972, 1-138.

2. J. Garnett, Bounded Analytic Functions. Academic Press. 1981, 1-467. (Also translated into Russian, 1984).

3. J. Garnett, Applications of Harmonic Measure. John Wiley & Sons, New York. 1986, 1-69.

4. J. Garnett, D.E. Marshall, Harmonic Measure. Cambridge University Press. 2005, 1-571.

5. J. Garnett, Bounded Analytic Functions, Revised First Edition. Springer Verlag. 2006, 1- 457.

Research Papers:

1. J. Garnett, Disconnected Gleason parts. Bull. Amer. Math. Soc., 72, 1966, 490-492.

2. J. Garnett, A topological characterization of Gleason parts. Pacific J. Math., 20, 1967, 59-63.

3. J. Garnett, I. Glicksberg, Algebras with the same multiplicative measures. J. Functional Analysis, 1, 1967, 331-341.

4. J. Garnett, On a theorem of Mergelyan. Pacific J. Math, 26, 1968, 461-467.

5. T.W. Gamelin, J. Garnett, Constructive techniques in rational approximation. Trans. Amer. Math. Soc., 143, 1969, 187-200.

6. J. Garnett, Positive length but zero analytic capacity. Proc. Amer. Math. Soc., 24, 1970, 696-699.

7. T.W. Gamelin, J. Garnett, Distinguished homomorphisms and fiber algebras. Amer. J. Math., 92, 1970, 455-474.

8. T.W. Gamelin, J. Garnett, Uniform approximation to bounded analytic functions. Rev. Un. Math. Argentina, 25, 1970, 87-94.

9. T.W. Gamelin, J. Garnett, Pointwise bounded approximation and hypodirichlet algebras. Bull. Amer. Math. Soc., 77, 1971, 137-141.

10. J. Garnett, Metric conditions for rational approximation. Duke Math. J., 37, 1970, 689-699.

11. T.W. Gamelin, J. Garnett, Pointwise bounded approximation and dirichlet algebras. J. Functional Analysis, 8, 1971, 360-404.

12. J. Garnett, Vitushkin's localization operator. Indiana Univ. Math. J., 20, 1971, 905-907.

13. J. Garnett, Interpolating sequences for bounded harmonic functions. Indiana Univ. Math. J., 21, 1971, 187-192.

14. T.W. Gamelin, J. Garnett, Bounded approximation by rational functions. Pacific J. Math., 45, 1973, 129-150.

15. A.M. Davie, T.W. Gamelin, J. Garnett, Distance estimates and pointwise bounded density. Trans. Amer. Math. Soc., 175, 1973, 37-68.

16. J. Garnett, On the Iversen-Tsuji theorem. Indiana Univ. Math. J., 24, 1974, 285-290.

17. J. Garnett, An estimate for line integrals and an application to distinguished homomorphisms. Illinois J. Math., 19, 1975, 537-541.

18. L. Carleson, J. Garnett, Interpolating sequences and separation properties. J. Analyse Math, 28, 1975, 273-299.

19. T.W. Gamelin, J. Garnett, L.A. Rubel, A.L. Shields, On badly approximable functions. J. Approximation Theory, 17, 1976, 280-296.

20. J. Garnett, A.G. O'Farrell, Sobolev approximation by a sum of subalgebras on the circle. Pacific J. Math., 65, 1976, 53-63.

21. J. Garnett, Two remarks on interpolation by bounded analytic functions. In Banach Spaces of Analytic Functions, J. Baker, C. Cleaver, and J. Diestel (eds.). Lecture notes in Mathematics, Springer-Verlag, 604, 1977, 32-40.

22. A. Bernard, J. Garnett, D.E. Marshall, Algebras generated by inner functions. J. Functional Analysis, 25, 1977, 275-285.

23. J. Garnett, P.W. Jones, The distance in BMO to $L^{|infty}$. . Ann. of Math., 108, 1978, 373-393.

24. J. Garnett, R.H. Latter, The atomic decomposition for Hardy spaces in several complex variables. Duke Math. J., 45, 1978, 815-845.

25. S.Y.A. Chang, J. Garnett, Analyticity of functions and subalgebras of $L^{\infty}$ containing $H^{\infty}.$ Proc. Amer. Math. Soc., 72, 1978, 41-45.

26. J. Garnett, Harmonic interpolating sequences, $L^p$ and BMO. Ann. Inst. Fourier (Grenoble), 28, 1978, 215-228.

27. J. Garnett, Some open problems concerning $H^\infty$" and BMO. Research on Linear Operators and Function Theory, 99 Unsolved Problems of Linear and Complex Analysis (Nikolskii, Havin and Kruschev (eds.), Seminar Notes Series, Steklov Mathematical Institute, Leningrad Division, 81, 1978, 228-229.

28 . J. Garnett, Two constructions in BMO. Proc. of Symposia in Pure Math., 35, 1979, 295-301.

29. J. Garnett, P.W. Jones, BMO from dyadic BMO. Pacific J. Math. , 99, 1982, 351-371.

30. J. Garnett, F.W. Gehring, P.W. Jones, Conformally invariant length sums. Indiana Univ. Math. J., 32, 1983, 809-829.

31. J. Garnett, E. Trubowitz, Gaps and bands of one dimensional periodic Schrodinger operators. Comment. Math. Helvetici, 59, 1984, 258-312.

32. A. Carbery, S.Y.A. Chang, J. Garnett, Weights and LlogL. Pac. J. Math., 120, 1985, 33-45.

33. J. Garnett, P.W. Jones, The corona theorem for Denjoy domains. Acta Math., 155, 1985, 27-40.

34. J. Garnett, E. Trubowitz, Gaps and bands of one dimensional periodic Schrodinger operators, II. Comment. Math. Helvetici, 62, 1987, 18-37.

35. J. Garnett, Corona problems, Interpolation problems, and inhomogeneous Cauchy-Riemann equations. Proc. of the International Congress of Math. Berkeley, 1986, 917-923.

36. C.J. Bishop, L. Carleson, J. Garnett, P.W. Jones, Harmonic measures supported on curves. Pac. J. of Math., 138, 1989, 233-236.

37. J. Garnett, F.W. Gehring, P.W. Jones, Quasiconformal groups and the conical set limit. Holomorphic functions and moduli, Vol. II, Berkeley, Cal. MSRI Pub. 11, Springer Verlag, 1988, 59-67.

38. J. Garnett, M. Papadimitrakis, Almost isometric maps of the hyperbolic plane. J. London Math. Soc., 43, 1991, 269-282.

39. J.B. Garnett, P.W. Jones, D.E. Marshall, A Lipschitz decomposition of minimal surfaces. J. Differential Geometry, 35, 1992, 659-673.

40. J. Garnett, S. Yang, Quasiextremal distance domains and integrability of derivatives of conformal mappings. Mich. Math. Journal, 41, 1994, 389-406.

41. J. Garnett, A. Nicolau, Interpolating Blaschke Products Generate $H^{\infty}$. Pacific J. of Math., 173, 1996, 501-510.

42. J. Garnett, S. Yoshinobu, Large sets of zero analytic capacity . Proc. A. M. S. 129, 2001, 3543-2548.

43. J. Garnett, J. Verdera, Analytic capacity, bilipshitz maps and Cantor sets . Math. Research Let. 10, 2003, 515-522.

44. J. Garnett, Featured Review of Painleve's problam and the semiadditivity of analytic capacity, by X. Tolsa. Mathematical Reviews, 2005.
(MR1982794 (2005c:300020) .

45. J. Garnett, L. Prat, X. Tolsa, Lipschitz Harmonic Capacity and Bilipschitz Images of Cantor Sets. Math. Research Let. 13, 2006, 865-884.

46. J. Garnett, T. Le, Y. Meyer, L. Vese, Image Decompositions Using Bounded Variation and Generalized Homogeneous Besov Spaces,
Comput. Harmon. Anal. 23 (2007), pp. 25-56.

47. J. Garnett, Review of Harmonic Measure, Geometric and Analytic Points of View, by L. Capogna, C. Kenig and L. Lanzani, Bulletin of the AMS, Invited Review. 45, 2008,
321-327.

48. J. B. Garnett, P. W. Jones, T. M. Le, and L. A. Vese, Modeling oscillatory components with the homogeneous spaces $BMO^{\alpha}$ and $W^{-\alpha,p}$
Pure and Applied Math. Quarterly, 7, (2011), 275-318.

49. J. Garnett, R. Killip, R. Schul, A doubling measure on R^d can charge a rectifiable curve, Proc. AMS, 138, 2010, 1673-1679.

50. Andrea L. Bertozzi, John B. Garnett, and Thomas Laurent, Characterization of radially symmetric finite time blowup in multidimensional aggregation equations, SIAM J. Math. Anal., 44(2), 2012, 651-681.

51. Hayden Schaeffer, John Garnett, and Luminita Vese, A texture model based on a concentration of measure, Inverse Probl. Imaging 7 (2013), no. 3, 927.946.

52. Yunho Kim, John Garnett, and Luminita Vese, Image restoration using one-dimensional Sobolev norm profiles of noise and texture, SIAM J. Imaging Sci., 7 (2014), no. 1, 366.390.

53. Vasileios Chousionis, John Garnett, Triet Le, and Xavier Tolsa Square functions and uniform rectifiablity, Trans. Amer. Math. Soc., 368 (2016) no. 9, 6064-6102.

54. Andrea Bertozzi, John Garnett, Thomas Laurent, and Joan Verdera, The regularity of the boundary of a multidimensional aggregation patch, SIAM J. Math. Anal. 48 (2016), no. 6. 3789-3819. arXiv:1507.07831.

55. John Garnett, Mihalis Mourgoglou, and Xavier Tolsa, Uniform rectifiability from Carleson measure estimates and $\epsilon$-approximability of bounded harmonic functions, Duke Math. Jour. 167, (2018), 1473-1524.

Work in Progress:

1. John B. Garnett, Triet M. Le, and Luminita A. Vese, Image Processing Variations with Analytic Kernels, arXiv:1204.1097.

2. Jonas Azzam, John Garnett, Mihalis Mourgoglou, and Xavier Tolsa, Uniform rectifiability, elliptic measure, square functions, and $\epsilon$-approximatility via an ACF monotinicity formula, arXiv:1612.02650, (to appear Int. Math. Res. Not. 2021).

3. John Garnett , Carleson measure estimates and $\epsilon$-approximatility for bounded harmonic functions, without Ahlfors regularity assumptions, arXiv:2006.10682, (to appear Rev. Mat. Iberoam).