L-BMO bounds for pseudo-multipliers associated with the harmonic oscillator

• Autores: Duván Cardona
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 54, Nº. 2, 2020, págs. 93-108
• Idioma: inglés
• DOI: 10.15446/recolma.v54n2.93828
• Títulos paralelos:
  • Continuidad L-BMO para pseudomultiplicadores asociados con el oscilador armónico
• Enlaces
  • Texto completo
• Resumen
  • español

    En esta nota se investigan condiciones de tipo Hörmander-Mihlin para garantizar la continuidad L-BMO de pseudomultiplicadores asociados con el oscilador armónico. También se estudia la continuidad de tipo $H^-L^1 para multiplicadores de Hermite.

  • English

    In this note we investigate some conditions of Hörmander-Mihlin type in order to assure the L∞-BMO boundedness for pseudo-multipliers of the harmonic oscillator. The H1-L1 continuity for Hermite multipliers also is investigated.

• Referencias bibliográficas
  • S. Bagchi and S. Thangavelu, On Hermite pseudo-multipliers, J. Funct. Anal. 268 (2015), no. 1, 140-170.
  • S. Blunck, A Hörmander-type spectral multiplier theorem for operators without heat kernel, Ann. Sc. Norm. Super. Pisa Cl. Sci. 5 (2003), no....
  • D. Cardona, A brief description of operators associated to the quantum harmonic oscillator on Schatten-von Neumann classes, Rev. Integr. Temas...
  • D. Cardona, Lp-estimates for a Schrödinger equation associated with the harmonic oscillator., Electron. J. Differential Equations (2019),...
  • D. Cardona, Sharp estimates for the Schrödinger equation associated to the twisted Laplacian, Rep. Math. Phys. (to appear), arXiv:1810.02940.
  • D. Cardona and E. S. Barraza, On nuclear lp multipliers associated to the harmonic oscillator, Perspectives from Developing Countries, Springer...
  • P. Chen, E. M. Ouhabaz, A. Sikora, and L. Yan, Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz...
  • P. Duren, B. Romberg, and A. Shields, Linear functionals on hp spaces with 0 < p < 1, J. Reine Angew. Math. 238 (1969), 32-60.
  • J. Epperson, Hermite multipliers and pseudo-multipliers, Proc. Amer. Math. Soc. 124 (1996), no. 7, 2061-2068.
  • C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587-588.
  • C. Fefferman and E. Stein, hp-spaces of several variables, Acta Math 129 (1972), 137-193.
  • G. H. Hardy, The mean value of the modulus of an analytic function, Proc. London Math. Soc. 14 (1914), 269-277.
  • L. Hörmander, Pseudo-differential operators and hypo-elliptic equations, Proc. Symposium on Singular Integrals, Amer. Math. Soc. 10 (1967),...
  • L. Hörmander, The analysis of the linear partial differential operators vol. iii., Springer-Verlag, 1985.
  • F. John and L. Nirenberg, On Functions of Bounded Mean Oscillation, Comm. Pure Appl. Math. (1961), 415-426.
  • M. Ruzhansky and D. Cardona, Hörmander condition for pseudomultipliers associated to the harmonic oscillator, arXiv:1810.01260.
  • M. Ruzhansky and N. Tokmagambetov, Nonharmonic analysis of boundary value problems without WZ condition, Math. Model. Nat. Phenom. 12 (2017),...
  • B. Simon, Distributions and their hermite expansions, J. Math. Phys. 12 (1971), 140-148.
  • S. Thangavelu, Multipliers for hermite expansions, Revist. Mat. Ibero. 3 (1987), 1-24.
  • S. Thangavelu, Lectures on Hermite and Laguerre Expansions, Math. Notes, vol. 42, Princeton University Press, Princeton, 1993.
  • S. Thangavelu, Hermite and special Hermite expansions revisited, Duke Math. J. 94 (1998), no. 2, 257-278.
  • N. Tokmagambetov and M. Ruzhansky, Nonharmonic analysis of boundary value problems, Int. Math. Res. Notices 12 (2016), 3548-3615.
  • T. Walsh, The dual of Hp(Rn+1+) for p < 1, Can. J. Math. 25 (1973), 567-577.