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Carlos Segovia Fernández

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Recent Developments in Real and Harmonic Analysis

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Abstract

It is an entirely vain endeavor to try to describe in a few pages the mathematical life of Carlos Segovia. The variety and richness of his deep results and proofs would need a whole book in order to put them into their propercontext and to see what has been their ulterior influence. However, space limitation has the advantage that this chapter will probably be read by more people than if the exposition was as exhaustive as it deserves. This chapter has been written keeping in mind the idea of reaching more people than just the specialists. It can be thought of as a painting in which only a reduced number of strokes have been made, enough to give the viewer a rough idea of the completed work, but giving him the freedom to choose to finish those parts in which he is more interested.

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References

  1. Abu-Falahah I., Macías R.A., Segovia C., Torrea J.L.: Transferring strong boundedness among Laguerre orthogonal systems. Proc. Indian Acad. Sci. Math. Sci. (to appear).

    Google Scholar 

  2. Aguilera N., Segovia C.: Weighted norm inequalities relating the \(g_{\lambda}^{\ast}\) and the area functions. Studia Math. 61 (1977), 293–303.

    MATH  MathSciNet  Google Scholar 

  3. Benedek A., Calderón A.P., Panzone R.: Convolution operators on Banach-space valued functions. Proc. Nat. Acad. Sci. USA 48 (1962), 356–365.

    Article  MATH  Google Scholar 

  4. Benedek A., Panzone, R., Segovia, C.: On operations of convolution type and orthonormal systems on compact abelian groups. Rev. Un. Mat. Argentina 22 (1964), 57–73.

    MATH  MathSciNet  Google Scholar 

  5. Bollobás B.: Martingale inequalities. Math. Proc. Cambridge Philos. Soc. 87 (1980), 377–382.

    Article  MATH  MathSciNet  Google Scholar 

  6. Calderón A.P.: Commutators of singular integral operators. Proc. Nat. Acad. Sci. USA 53 (1965), 1092–1099.

    Article  MATH  Google Scholar 

  7. Calderón A.P., Zygmund A.: On the existence of certain singular integrals. Acta Math. 88 (1952), 85–139.

    Article  MATH  MathSciNet  Google Scholar 

  8. Calderón A.P., Zygmund A.: On singular integrals. Amer. J. Math. 78 (1956), 289–300.

    Article  MATH  MathSciNet  Google Scholar 

  9. Capri O.N., Segovia, C. : Behaviour of L r-Dini singular integrals in weighted L 1 spaces. Studia Math. 92 (1989), no. 1, 21–36.

    MathSciNet  Google Scholar 

  10. Capri O.N., Segovia, C.: Convergence of singular integrals in weighted L 1 spaces. Pro. Mathematica, 3 no. 5 y 6, 3–29.

    Google Scholar 

  11. Carleson L., Jones P.: Weighted norm inequalities and a theorem of Koosis. Mittag-Leffler Institute, Report 2, 1981.

    Google Scholar 

  12. Coifman R.R., Rochberg R., Weiss G.: Factorization theorems for Hardy spaces in several variables.. Ann. of Math. (2) 103 (1976), no. 3, 611–635.

    Article  MATH  MathSciNet  Google Scholar 

  13. Coifman R.R., Weiss G.: Analyse harmonique non-commutative sur certain espaces homogenes. Lecture Notes in Mathematics, 242, Springer-Verlag, Berlin, 1971.

    Google Scholar 

  14. Forzani L., Harboure E., Scotto R.: Harmonic analysis related to Hermite expansions. This volume.

    Google Scholar 

  15. García-Cuerva J., Harboure E., Segovia C., Torrea J.L.: Weighted norm inequalities for commutators of strongly singular integrals. Indiana Univ. Math. J. 40 (1991), 1397–1420.

    Article  MATH  MathSciNet  Google Scholar 

  16. Gatto A.E., Gutierrez C.: On weighted norm inequalities for the maximal functions. Studia Math. 76 (1983), no. 1, 59–62.

    MATH  MathSciNet  Google Scholar 

  17. Gatto A.E., Jimenez J.R., Segovia C.: On the solution of the equation D m F = f for fH p, Conference on Harmonic Analysis in Honor of Antoni Zygmund, Vol. II, Wadsworth Mathematical Series (1983), 392–415.

    Google Scholar 

  18. Gatto A.E., Segovia C.: Product rule and chain rule estimates for the Hajtasz gradient on doubling metric measure spaces. Colloq. Math. 105 (2006), no. 1, 19–24.

    Article  MATH  MathSciNet  Google Scholar 

  19. Gatto A.E., Segovia C., Vagi S.: On fractional differentiation and integration on spaces of homogeneous type. Rev. Mat. Iberoamericana 12 (1996), 111–145.

    Article  MATH  MathSciNet  Google Scholar 

  20. Gundy R.F.: Sur les transformations de Riesez pour le semi-groupe d'Ornstein-Uhlenbeck. C.R. Acad. Sci. Paris Sr. I Math. 303 (1986), no. 19, 967–970.

    MATH  MathSciNet  Google Scholar 

  21. Gutiérrez C.E.: On the Riesz transforms for Gaussian measures. J. Funct. Anal. 120 (1994), no. 1, 107–134.

    Article  MATH  MathSciNet  Google Scholar 

  22. Gutiérrez C.E., Segovia C., Torrea J.L.: On higher Riesz transforms for Gaussian measures. J. Fourier Anal. Appl. 2 (1996), 583–596.

    Article  MATH  MathSciNet  Google Scholar 

  23. Harboure E., Macías R., Segovia C.: Boundedness of fractional operators on L p spaces with different weights. Trans. Amer. Math. Soc. 285 (1984), 629–647.

    MATH  MathSciNet  Google Scholar 

  24. Harboure E., Macías R., Segovia C.: A two weight inequality for the fractional integral when p = n/α. Proc. Amer. Math. Soc. 90 (1984), 555–562.

    MATH  MathSciNet  Google Scholar 

  25. Harboure E., Macías R., Segovia C.: Extrapolation results for classes of weights. Amer. J. Math. 110 (1988), 383–397.

    Article  MATH  MathSciNet  Google Scholar 

  26. Harboure E., Macías R., Segovia C.: An extrapolation theorem for pairs of weights. Rev. Un. Mat. Argentina 40 (1997), no. 3–4, 37–48.

    MATH  MathSciNet  Google Scholar 

  27. Harboure E., Macías R.A., Segovia C., Torrea J.L.: Some estimates for maximal functions on Köthe function spaces. Israel J. Math. 90 (1995), 349–371.

    Article  MATH  MathSciNet  Google Scholar 

  28. Harboure E., de Rosa L., Segovia C., Torrea, J.L.: L p-dimension free boundedness for Riesz transforms associated to Hermite functions. Math. Ann. 328 (2004), no. 4, 653–682.

    Article  MATH  MathSciNet  Google Scholar 

  29. Harboure E., Segovia C., Torrea J.L.: Boundedness of commutators of fractional and singular integrals for the extreme values of p. Illinois J. Math. 41 (1997), 676–700.

    MathSciNet  Google Scholar 

  30. Harboure E., Segovia C., Torrea J.L., Viviani B.: Power weighted L p-inequalities for Laguerre Riesz transforms. Arkiv Math. 46 (2008), 285–313.

    Article  MATH  MathSciNet  Google Scholar 

  31. Hunt R.A., Muckenhoupt B., Wheeden R.L.: Weighted norm inequalities for the conjugate function and Hilbert transform. Trans. Amer. Math. Soc. 176 (1973), 227–251.

    Article  MATH  MathSciNet  Google Scholar 

  32. Macías R., Segovia C.: Weighted norm inequalities for parabolic fractional integrals. Studia Math. 61 (1977), 279–291.

    MATH  MathSciNet  Google Scholar 

  33. Macías R., Segovia C.: Lipschitz functions on Spaces of Homogeneous Type. Adv. Math. 33 (1979), 257–270.

    Article  MATH  Google Scholar 

  34. Macías R., Segovia C.: A decomposition into atoms of distributions on spaces of homogeneous type. Adv. Math. 33 (1979), 271–309.

    Article  MATH  Google Scholar 

  35. Macías R., Segovia C.: A well-behaved quasi-distance for spaces of homogeneous type. Trabajos de Matemática, Serie I 32 (1981), IAM - CONICET, Buenos Aires.

    Google Scholar 

  36. Macías R., Segovia C., Torrea J.L.: Singular integral operators with non-necessarily bounded kernels on spaces of homogeneous type. Adv. Math. 93 (1992), 25–60.

    Article  MATH  MathSciNet  Google Scholar 

  37. Macías R.A., Segovia C., Torrea J.L.: Heat-diffusion maximal operators for Laguerre semigroups with negative parameters. J. Funct. Anal. 229 (2005), no. 2, 300–316.

    Article  MATH  MathSciNet  Google Scholar 

  38. Macías R.A., Segovia C., Torrea J.L.: Weighted norm estimates for the maximal operator of the Laguerre functions heat diffusion semigroup. Studia Math. 172 (2006), 149–167.

    Article  MATH  MathSciNet  Google Scholar 

  39. Martin-Reyes F.J., Ortega P., de la Torre A.: Weights for one-sided operators, This volume.

    Google Scholar 

  40. Meyer, P.-A.: Transformations de Riesz pour les lois gaussiennes. Seminar on probability, XVIII, 179–193, Lecture Notes in Math., 1059, Springer, Berlin, 1984.

    Google Scholar 

  41. Muckenhoupt B.: Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972), 207–226.

    Article  MATH  MathSciNet  Google Scholar 

  42. Ombrosi S., Segovia C.: One-sided singular integral operators on Calderón-Hardy spaces. Rev. Un. Mat. Argentina 44 (2003), no. 1, 17–32.

    MATH  MathSciNet  Google Scholar 

  43. Ombrosi S., Segovia C., Testoni R.: An interpolation theorem between one-sided Hardy spaces. Ark. Mat. 44 (2006), no. 2, 335–348.

    Article  MATH  MathSciNet  Google Scholar 

  44. Panzone R., Segovia, C.: Measurable transformations on compact spaces and O. N. systems on compact groups. Rev. Un. Mat. Argentina 22 (1964), 83–102.

    MATH  MathSciNet  Google Scholar 

  45. Pisier G.: Riesz transforms: a simpler analytic proof of P.-A. Meyer's inequality. Séminaire de Probabilités, XXII, 485–501, Lecture Notes in Math., 1321, Springer, Berlin, 1988.

    MathSciNet  Google Scholar 

  46. de Rosa L., Segovia C.: Convergence of truncated singular integrals with two weights. Colloq. Math., 60/61 (1990), 579–591.

    MathSciNet  Google Scholar 

  47. de Rosa L., Segovia, C.: Convergence in L 1 of singular integrals with nonstandard truncations. Rev. Un. Mat. Argentina 38 (1993), no. 3–4, 246–255.

    MATH  MathSciNet  Google Scholar 

  48. de Rosa L., Segovia C.: Weighted H p spaces for one sided maximal functions. Harmonic analysis and operator theory (Caracas, 1994), 161–183, Contemp. Math., 189, Amer. Math. Soc., Providence, RI, 1995.

    Google Scholar 

  49. de Rosa L., Segovia C.: Dual spaces for one-sided weighted Hardy spaces. Rev. Un. Mat. Argentina 40 (1997), 49–71.

    MATH  MathSciNet  Google Scholar 

  50. de Rosa L., Segovia C.: One-sided Littlewood-Paley theory. Proceedings of the conference dedicated to Professor Miguel de Guzmán (El Escorial, 1996), J. Fourier Anal. Appl. 3 (1997), Special Issue, 933–957

    Article  MATH  MathSciNet  Google Scholar 

  51. de Rosa, L., Segovia, C.: One-sided Littlewood–Paley theory. J. of Fourier Anal. and Appl. 3 (1997), 933–957.

    Article  MATH  MathSciNet  Google Scholar 

  52. de Rosa L., Segovia C.: A substitute of harmonic majorization. Indiana Univ. Math. J. 48 (1999), 1535–1545.

    MATH  MathSciNet  Google Scholar 

  53. de Rosa L., Segovia C.: Equivalence of norms in one-sided H p spaces. Collect. Math. 53 (2002), no. 1, 1–20.

    MATH  MathSciNet  Google Scholar 

  54. de Rosa L., Segovia C.: Some weighted norm inequalities for a one-sided version of \(g_{\lambda}^{\ast}\). Studia Math. 176 (2006), no. 1, 21–36.

    Article  MATH  MathSciNet  Google Scholar 

  55. Rubio de Francia J.L.: Weighted norm inequalities and vector-valued inequalities. Harmonic Analysis Lecture Notes in Math. 908, Springer 1982, 86–101.

    Article  MathSciNet  Google Scholar 

  56. Rubio de Francia J.L.: Factorization and extrapolation of weights. Amer. J. math. 110 (1984), 533–547.

    Article  MathSciNet  Google Scholar 

  57. Rubio de Francia J.L., Torrea J.L.: Some Banach techniques in vector-valued Fourier Analysis. Colloquium Math. 54 (1976), 273–284.

    MathSciNet  Google Scholar 

  58. Sawyer, E.: Weighted inequalities for the one-sided Hardy-Littlewood maximal functions. Trans. Amer. Math. Soc. 297 (1986), no. 1, 53–61.

    Article  MATH  MathSciNet  Google Scholar 

  59. Segovia C., On the area function of Lusin. Doctoral dissertation. The University of Chicago (1967).

    Google Scholar 

  60. Segovia C.: On the area function of Lusin. Studia Math. 33 (1969), 311–343.

    MATH  MathSciNet  Google Scholar 

  61. Segovia, C.: Sobre la teoría de la extrapolación. Anales Acad. Nac. Cs. Exactas, Fís. y Nat. Argentina, 42 (1990), 31–34.

    Google Scholar 

  62. Segovia, C.: Estado actual de la matemática en la Argentina, II. Encuentro Hispanoanericano de Historia de las Ciencias, Real Academia de Ciencias, España, y Academia Nacional de Ciencias Exactas, Físicas y Naturales, Argentina, Madrid, (1991).

    Google Scholar 

  63. Segovia, C.: Hardy spaces and atomic decompositions. Proceedings of the Second “Dr. António A. R. Monteiro” Congress on Mathematics (Bahía Blanca, 1993), 95–103, Univ. Nac. del Sur, Bahía Blanca, 1993.

    Google Scholar 

  64. Segovia, C.: Extrapolation and commutators of singular integrals. Atas do 40 Seminario Brasileiro de Análise (1994), 165–190.

    Google Scholar 

  65. Segovia C., Testoni R. : One-sided strongly singular operators. Preprint.

    Google Scholar 

  66. Segovia C., Testoni R.: A multiplier theorem for one-sided Hardy spaces. Proc. Roy. Soc. Edinburgh Sect. A (to appear).

    Google Scholar 

  67. Segovia C., Torrea J.L.: A note on the commutator of the Hilbert transform. Rev. Un. Mat. Argentina 35 (1989), 259–264 (1991).

    MATH  MathSciNet  Google Scholar 

  68. Segovia C., Torrea J.L.: Weighted inequalities for commutators of fractional and singular integrals. Conference on Mathematical Analysis (El Escorial, 1989). Publ. Mat. 35 (1991), no. 1, 209–235.

    Article  MATH  MathSciNet  Google Scholar 

  69. Segovia C., Torrea J.L.: Vector-valued commutators and applications. Indiana Univ. Math. J. 38 (1989), 959–971.

    Article  MATH  MathSciNet  Google Scholar 

  70. Segovia C., Torrea J.L.: Extrapolation for pairs of related weights. Analysis and partial differential equations, 331–345, Lecture Notes in Pure and Appl. Math., 122, Dekker, New York, 1990.

    Google Scholar 

  71. Segovia C., Torrea J.L.: Commutators of Littlewood-Paley sums. Ark. Mat. 31 (1993), 117–136.

    Article  MATH  MathSciNet  Google Scholar 

  72. Segovia C., Torrea J.L.: Higher order commutators for vector-valued Calderón-Zygmund operators. Trans. Amer. Math. Soc. 336 (1993), 537–556.

    MATH  MathSciNet  Google Scholar 

  73. Segovia C., Wheeden R.: On certain fractional area integrals. J. Math. Mech. 19 1969/1970, 247–262.

    MathSciNet  Google Scholar 

  74. Segovia C., Wheeden R.: On the function \(g_{\lambda}^{\ast}\) and the heat equation. Studia Math. 37 (1970), 57–93.

    MATH  MathSciNet  Google Scholar 

  75. Segovia C., Wheeden R.: Fractional differentiation of the commutator of the Hilbert transform. J. Functional Analysis 8 (1971), 341–359.

    Article  MATH  MathSciNet  Google Scholar 

  76. Segovia C., Wheeden R.: On weighted norm inequalities for the Lusin area integral. Trans. Amer. Math. Soc. 176 (1973), 103–123.

    Article  MATH  MathSciNet  Google Scholar 

  77. Stein E. M.: Singular integrals and differentiability properties of functions. Princeton University Press, 1970.

    MATH  Google Scholar 

  78. Stein E. M.: The development of square functions in the work of A. Zygmund. Bull. Amer. Math. Soc. 2 (1982), 359–376.

    Article  Google Scholar 

  79. Stein E. M.: Singular integrals: the roles of Calderón and Zygmund. Notices Amer. Math. Soc. 45 (1998), no. 9, 1130–1140.

    MATH  MathSciNet  Google Scholar 

  80. Stempak, K. : Heat-diffusion and Poisson integrals for Laguerre expansions. Tohoku Math. J. (2), 46 (1994), no. 1, 83–104.

    Article  MATH  MathSciNet  Google Scholar 

  81. Szego G., Orthogonal polynomials. Amer. Math. Soc. Colloquium Publication XXIII, American Mathematical Society, 1939.

    Google Scholar 

  82. Thangavelu S.: Lectures on Hermite and Laguerre expansions. Mathematical Notes 24. Princeton University Press, 1993.

    Google Scholar 

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Macías, R.A., Torrea, J.L. (2010). Carlos Segovia Fernández. In: Cabrelli, C., Torrea, J. (eds) Recent Developments in Real and Harmonic Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4588-5_1

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