Publications

List of Publications

Rodolfo H. Torres. .

Books and Books Edited

  1. Boundedness results for operators with singular kernels on distribution spaces, Mem. Amer. Math. Soc., 442 (1991), 178 pages.
  2. Harmonic Analysis, Partial Differential Equations, and Related Topics (co-editor with E. Gavosto, M. Korten, and C. Moore), AMS Contemporary Mathematics Series, #428, 2007.

Book chapters

  1. The sampling theorem, phi-transform, and Shannon Wavelets for R, Z, T and Z subscript N (with M. Frazier), in Wavelets: Mathematics and Applications, CRC Press, Boca Raton, Florida, 1993.
  2. (a) Regularity and approximations results for the Maxwell problem on C superscript one and Lipschitz domains (with M. Mitrea and G. Welland), (b) Open Problem (with G. Welland), in Clifford Algebras in Analysis and Related Topics, CRC Press, Boca Raton, Florida, 1995.
  3. The analysis of oscillatory behavior in signals through their samples, in Modern Sampling Theory: Mathematics and Applications, J. Benedetto and P. Ferreira Eds., Birkhauser, 2001.
  4. Fourier blues: structural coloration of biological tissues (with R. Prum), Excursions in harmonic analysis. Volume 2, 401-421, Appl. Numer. Harmon. Anal., Birkhäuser-Springer, New York, 2013.
  5. Cora Sadosky: Her mathematics, mentorship, and professional contributions, Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory. Celebrating Cora Sadosky’s Life. Volume 1, Celebrating Cora Sadosky’s. M. C. Pereyra, S. Marcantognini, A. M. Stokolos, W. Urbina, (Eds.), Springer, 2016.
  6. Multilinear weighted norm inequalities under integral type regularity conditions (with L. Chaffee and X. Wu), Harmonic Analysis, Partial Differential Equations and Applications In Honor of Richard L. Wheeden. S. Chanillo, B. Franchi, G. Lu, C. Perez, E. T. Sawyer, (Eds.), Springer, 2017.
  7. The discrete Calderón reproducing formula of Frazier and Jawerth (with A. Bényi), Functional Analysis, Harmonic Analysis, and Image Processing: A Collection of Papers in Honor of Björn Jawerth, M. Cwikel and M. Millman (Eds.), Contemporary Mathematics Volume: 693; AMS, 2017.

Articles

  1. The Boundedness of Calderón-Zygmund operators on the spaces F dot, subscript p, superscript alpha comma q (with M. Frazier and G. Weiss), Rev. Mat. Iberoamericana, 4 (1988), 41-72.
  2. Continuity properties of pseudodifferential operators of type 1,1, Comm. Partial Diff. Eq., 15 (1990), 1313-1328.
  3. Spaces of sequences, sampling theorem and functions of exponential type, Studia Math., 100 (1991), 51-74.
  4. Singular integral equations, spaces of homogeneous type, and boundary elements in non-smooth domains (with V. Adolfsson and B. Jawerth), Rev. U. Math. Arg., 37 (1991), 163-183.
  5. The Helmholtz equation and transmission problems with Lipschitz interfaces (with G. Welland), Indiana University Math. J., 42 (1993), 1457-1485.
  6. A boundary integral method for parabolic equations in nonsmooth domains (with V. Adolfsson and B. Jawerth), Comm. Pure Appl. Math., 47 (1994), 861-892.
  7. Layer potential operators and a space of boundary data for electromagnetism in nonsmooth domains (with G. Welland), Michigan Math. J. 43 (1996), 189-206.
  8. A transmission problems in the scattering of electromagnetic waves by a penetrable object, SIAM J. Math. Anal., 27 (1996), 1406-1423.
  9. Sampling and nonlinear approximation of band limited signals in mean oscillation spaces, Proc. SAMPTA 97, Aveiro, Portugal, 1997.
  10. Maxwell’s equations and dielectric obstacles with Lipschitz boundaries, J. London Math. Soc., 57 (1998), 157-169.
  11. Mean oscillation of functions and the Paley-Wiener space, J. Fourier Anal. and Appl., 4 (1998), 283-297.
  12. Coherent light scattering by blue feather barbs (with R. Prum, S. Willamson, and J. Dyck), Nature, 396 (1998), 28-29.
  13. Two-dimensional Fourier analysis of the spongy medullary keratin of structurally coloured feather barbs (with R. Prum, S. Willamson, and J. Dyck), Proc. Royal Society: Biological Sciences (B) 266 (1999), 13-22.
  14. Pseudodifferential operators with homogeneous symbols (with L. Grafakos), Michigan Math. J. 46 (1999), 261-269.
  15. Coherent light scattering by nanostructures collagen arrays in the cranucles of the Malagasy Asities (Eurylaimidae: Aves), (with R. Prum, C. Kovach, S. Willamson, and S. Goodman), Journal of Experimental Biology, 202 (1999), 3507-3522.
  16. A multilinear Schur test and multiplier operators (with L. Grafakos), J. Func. Anal. 187 (2001), 1-24.
  17. Azul de ave. Un color estructural (with R. Prum), Investigación y Ciencia (Spanish edition of Scientific American) 299 (2001), 36-37.
  18. Azul de ave. Un color estructural (with R. Prum), Reprinted in Temas Investigación y Ciencia: El color, 27 (2002), 30-31.
  19. Discrete decomposition for bilinear operators and almost diagonal conditions (with L. Grafakos), Trans. Amer. Math. Soc. 354 (2002), 1153-1176.
  20. Multilinear Calderón-Zygmund theory (with L. Grafakos), Adv. in Math. 165 (2002), 124-164.
  21. On multilinear singular integrals of Calderón-Zygmund type (with L. Grafakos), Publ. Mat. Vol. extra (2002), 57-91.
  22. Maximal operator and weighted norm inequalities for multilinear singular integrals (with L. Grafakos), Indiana University Math. J. 51 (2002), 1261-1276.
  23. Decomposition of B dot, subscript one, superscript zero comma one, of Z into special atoms (with S. Boza), Math. Nachr., 254/255 (2003), 3-10.
  24. Sharp maximal function estimates for multilinear singular integrals (with C. Pérez), Contemp. Math. 320 (2003), 323-331.
  25. Uniqueness in the inverse conductivity problem for conductivities with 3/2 derivatives in L superscript p, p greater than two n (with R. Brown), J. Fourier Anal. and Appl. 9 (2003), 563-574.
  26. Coherent light scattering of ultraviolet light by avian feather barbs (with R. Prum and S. Andersson), Auk 120 (2003), 163-170.
  27. Symbolic calculus for the transposes of bilinear pseudodifferential operators (with A. Bényi), Comm. Partial Diff. Eq. 28 (2003), 1161-1181.
  28. Structural colouration of avian skin: convergent evolution of coherently scattering dermal collagen arrays (with R. Prum), Journal of Experimental Biology 206 (2003), 2409-2429.
  29. A Fourier tool for the analysis of coherent light scattering by bio-optical nanostructures (with R. Prum), Integr. Comp. Biol. 43 (2003), 591-602.
  30. Almost orthogonality and a class of bounded bilinear pseudodifferential operators (with Á. Bényi), Math. Res. Lett. 11 (2004), 1-11.
  31. Structural colouration of mammalian skin: convergent evolution of coherently scattering dermal collagen arrays (with R. Prum), Journal of Experimental Biology 207 (2004), 2157-2172.
  32. Calderón-Zygmund operators on mixed Lebesgue spaces and applications to null forms (with A. Stefanov), J. London Math. Soc. 70 (2004), 447-462.
  33. Blue integumentary structural colours in dragonflies (Odonata) are not produced by incoherent Tyndall scattering (with R. Prum and J. Cole), Journal of Experimental Biology 207 (2004), 3999-4009.
  34. Análisis espectral de nanoestructuras en tejidos biológicos (with R. Prum) Matematicalia 1 no. 2 (2005), Matematicalia website.
  35. Anatomically Diverse Butterfly Scales Produce Structural Colors by Coherent Scattering (with R. Prum and T. Quinn), Journal of Experimental Biology 209 (2006), 748-765.
  36. Sobolev space estimate and symbolic calculus for bilinear pseudodifferential operators (with Á. Bényi and A. Nahmod), J. Geom. Anal. 16.3 (2006), 431-453.
  37. New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory (with A. Lerner, S. Ombrosi, C. Pérez, and R. Trujillo-González), Adv. in Math. 220, (2009) 1222-1264.
  38. Modulation invariant bilinear T(1) Theorem (with Á. Bényi, C. Demeter, A. Nahmod, and C. Thiele), J. Anal. Math. 109 (2009), 279-352.
  39. Multilinear singular integrals with variable coefficients, Rev. Un. Mat. Argentina 50 (2009), 153-170.
  40. Bilinear paraproducts revisited (with Á. Bényi, D. Maldonado, and A. Nahmod), Math. Nach. 283 (2010), 1257-1276.
  41. Sharp weighted bounds for fractional integral operators (with M. Lacey, K. Moen and C. Pérez), J. Func. Anal., 259 (2010), no. 5, 1073-1097.
  42. On the Hörmander classes of bilinear pseudodifferential operators (with Á. Bényi, D. Maldonado and V. Naibo), J. Integral Eq. Oper. Theory, 67 (2010), 341-364.
  43. The multilinear strong maximal function (with L. Grafakos, L. Liu, and C. Pérez), J. Geom. Anal. 21 (2011), no. 1, 118-149.
  44. Sobolev space estimates for a class of bilinear pseudodifferential operators lacking symbolic calculus (with F. Bernicot), Anal. PDE 4 (2011), 551-571.
  45. Rubio de Francia’s extrapolation Theory: estimates for the distribution function (with M. J. Carro and J. Soria), J. London Math. Soc. 85 (2012), 430-454.
  46. Compact bilinear operators and commutators (with A. Bényi), Proc. Amer. Math. Soc. 141 (2013), no. 10, 3609-3621.
  47. On the Hörmander classes of bilinear pseudodifferential operators II (with A. Bényi, F. Bernicot, D. Maldonado, and V. Naibo), Indiana Univ. Math. J. 62 (2013), no. 6, 1733-1764.
  48. End-point estimates for iterated commutators of multilinear singular integrals (with C. Pérez, G. Pradolini and R. Trujillo-González), Bull. London Math. Soc. (2014) 46 (1), 26-42.
  49. Minimal regularity conditions for the end-point estimate of bilinear Calderón-Zygmund operators (with C. Pérez), Proc. Amer. Math. Soc., Series B, 1 (2014), 1-13.
  50. Compactness properties of commutators of bilinear fractional integrals (with A. Bényi, W. Damian, and K. Moen), Math. Z. 280 (2015), no. 1-2, 569-582.
  51. Compact bilinear commutators: The weighted case (with A. Bényi, W. Damian, and K. Moen), Michigan Math. J. 64 (2015), no. 1, 39-51.
  52. Leibniz’s rule, sampling and wavelets on mixed Lebesgue spaces (with E. Ward), J. of Fourier Anal. and Appl. 21, (2015), no. 5, 1053-1076.
  53. Characterization of compactness of the commutators of bilinear fractional integral operators (with L. Chaffee), Potential Analysis, 43 (2015), no. 3, 481-494.
  54. Several results in classical and modern harmonic analysis in mixed Lebesgue spaces (with E. Ward), RIMS Kôkyôroku Bessatsu (Bessatsu) B65 (2017), 159-177.
  55. Smoothing Properties of Bilinear Operators and Leibniz-Type Rules in Lebesgue and Mixed Lebesgue Spaces, (with J. Hart and X. Wu), Trans. Amer. Math. Soc., 370 (2018), 8581-8612.
  56. Characterization of compactness of commutators of bilinear singular integral operators, (with L. Chaffee, P. Chen, Y. Han, and L. A. Ward), Proc. Amer. Math. Soc. 146 (2018), 3943-3953.
  57. Compact bilinear commutators: The quasi Banach space case (with Q. Xue and J. Yan), J. Anal. 26 (2018), 227-234.
  58. John-Nirenberg inequalities and weight invariant BMO spaces (with J. Hart), J. Geom. Anal. (2018), DOI: 10.1007/s12220-018-0054-y.
  59. Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach (with Á. Bényi, J. M. Martell, K. Moen, and E. Stachura), arXiv:1710.08515, Oct. 23, 2017, preprint.

Other publications

  1. Remembering Cora Sadosky (with E. A. Gavosto, A. Nahmod, C. Pereyra, G. Ponce, and W. Urbina), AWM Newsletter, Volume: 41 (2) 2011.
  2. Research Analytics: Facilitating the Use of Metrics to Improve the Research Profile of Academic Programs, Merrill Advanced Studies Center Report No. 117 (2013), 96-105.
  3. Why I Became a Mathematician, I, Mathematician, P. Casazza, S. G. Krantz, and R. D. Ruden (Eds), Mathematical Association of America, 2015.
  4. Enhancing and Automating University Reporting Of R&D Expenditure Data Using Machine Learning Techniques (with J. L. Rosenbloom, J. St. Amand, and A. Sadovsky), Merrill Advanced Studies Center Report No. 121 (2017), 35-46.
  5. New Challenges and Opportunities for International Research Collaborations on a More Level Playing Field, Merrill Advanced Studies Center Report No. 122, to appear.