New results on restriction of Fourier multipliers

• Autores: María Jesús Carro Rossell , Salvador Rodríguez López
• Localización: Mathematische zeitschrift, ISSN 0025-5874, Vol. 265, Nº. 2, 2010, págs. 417-435
• Idioma: inglés
• DOI: 10.1007/s00209-009-0522-y
• Texto completo no disponible (Saber más ...)
• Resumen

  • We develop an extension of the Transference methods introduced by R. Coifman and G. Weiss and apply it to study the problem of the restriction of Fourier multipliers between rearrangement invariant spaces, obtaining natural extensions of the classical de Leeuw's result and its further extension to maximal Fourier multipliers due to C. Kenig and P. Tomas.

• Referencias bibliográficas
  • Asmar N., Berkson E., Gillespie T.A.: Transference of strong type maximal inequalities by separation-preserving representations. Am. J. Math....
  • Asmar N., Berkson E., Gillespie T.A.: Transfert des opérateurs maximaux par des représentations conservant la séparation. C. R. Acad. Sci....
  • Asmar N., Berkson E., Gillespie T.A.: Transfert des multiplicateurs de type faible. C. R. Acad. Sci. Paris Sér. I Math. 311(3), 173–176 (1990)
  • Bennett C., Sharpley R.: Interpolation of operators. Pure and Applied Mathematics, vol. 129. Academic Press Inc., Boston (1988)
  • Berkson E., Blasco O., Carro M.J., Gillespie T.A.: Discretization and transference of bisublinear maximal operators. J. Fourier Anal. Appl....
  • Bernardis A.L., Martín-Reyes F.J.: Singular integrals in the Cesàro sense. J. Fourier Anal. Appl. 6(2), 143–152 (2000)
  • Blasco O., Carro M., Gillespie T.A.: Bilinear Hilbert transform on measure spaces. J. Fourier Anal. Appl. 11(4), 459–470 (2005)
  • Blasco O., Villarroya F.: Transference of bilinear multiplier operators on Lorentz spaces. Ill. J. Math. 47(4), 1327–1343 (2003)
  • Carro M., Soria J.: Transference theory on Hardy and Sobolev spaces. Colloq. Math. 74(1), 47–69 (1997)
  • Carro M.J., Raposo J.A., Soria J.: Recent developments in the theory of Lorentz spaces and weighted inequalities. Mem. Am. Math. Soc. 187(877),...
  • Carro M.J., Soria J.: Weighted Lorentz spaces and the Hardy operator. J. Funct. Anal. 112(2), 480–494 (1993)
  • Chandarana S.: Lp-bounds for hypersingular integral operators along curves. Pacific J. Math. 175, 389–416 (1996)
  • Coifman, R.R., Weiss, G.: Transference Methods in Analysis. American Mathematical Society, Providence (1976) (Conference Board of the Mathematical...
  • Cowling M.G., Fournier J.J.F.: Inclusions and noninclusion of spaces of convolution operators. Trans. Am. Math. Soc. 221(1), 59–95 (1976)
  • Fefferman C.: Inequalities for strongly singular convolution operators. Acta Math. 124, 9–36 (1970)
  • Feichtinger, H.G.: Banach convolution algebras of Wiener type. In: Functions, Series, Operators, vol. I, II (Budapest, 1980), Colloq. Math....
  • Feichtinger H.G., Luef F.: Wiener amalgam spaces for the fundamental identity of Gabor analysis. Collect. Math. Vol. Extra(1), 233–253 (2006)
  • Hardy G.H.: A theorem concerning Taylor’s series. Quart. J. Pure Appl. Math. 44, 147–160 (1913)
  • Hirschman I.I. Jr.: On multiplier transformations. Duke Math. J. 26, 221–242 (1959)
  • Kenig C.E., Tomas P.A.: Maximal operators defined by Fourier multipliers. Studia Math. 68(1), 79–83 (1980)
  • Laghi N., Lyall N.: Strongly singular integrals along curves. Pacific J. Math. 233(2), 403–415 (2007)
  • de Leeuw K.: On Lp multipliers. Ann. Math. 81(2), 364–379 (1965)
  • Raposo J.A.: Weak type (1,1) multipliers on LCA groups. Studia Math. 122(2), 123–130 (1997)
  • Seeger A., Tao T.: Sharp Lorentz space estimates for rough operators. Math. Ann. 320(2), 381–415 (2001)
  • Stein, E.M.: Singular integrals, harmonic functions, and differentiability properties of functions of several variables. In: Singular Integrals...
  • Wainger S.: Special trigonometric series in k-dimensions. Mem. Am. Math. Soc. No. 59, 102 (1965)