SciELO - Scientific Electronic Library Online

vol.30 número3A Note on Büchi's Problem for p-adic numbers índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados



Links relacionados


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.30 no.3 Antofagasta dic. 2011 

Proyecciones Journal of Mathematics Vol. 30, No 3, pp. 285-294, December 2011. Universidad Católica del Norte Antofagasta - Chile


Nonlinear Bessel potentials and generalizations of the Kato Class


René Erlin Castillo

Universidad Nacional de Colombia, Colombia




We study the scale of function spaces Mp introduced by Zamboni. For these spaces, we get a characterization in terms of nonlinear Bessel potentials. This result is based on a known characterization of the Kato class Kn,s of order s in terms of Bessel potentials and the space of bounded uniformly continuous functions.


AMS Classification: 31C45.

Keywords :Kato class, Bessel potentials, nonlinear potential.


 Texto completo sólo en formato PDF



[1] Adams D. R. and Hedberg, L. I., Function Spaces and Potential Theory, Springer Verlag, (1996)        [ Links ]

[2] Aizenman, M. and Simon, Brownian motion and Harnack's inequality for Schrödinger operators, Comm. Pure Appl. Math. 35, 209-271, (1982).         [ Links ]

[3] Bourbaki, N., Elements of Mathematics, General Topology, part 1, Addison-Wesley, Publishing Company, (1966).         [ Links ]

[4] Davies, E. B. and Hinz, A., Kato class potentials for higher order elliptic operators, J. London Math. Soc. (2) 58, pp. 669-678, (1998).         [ Links ]

[5] Gulisashvili, A., On the Kato classes of distributions and the BMO-classes, In: Differential Equations and Control Theory (Aizicovici, S. et al., eds), Lect. Notes Pure Appl. Math. 225, Marcel Dekker, New York, pp. 159-176, (2002).         [ Links ]

[6] ____________, Sharp estimates in smoothing theorems for Schrödinger semigroups, J. Functional Analysis. 170, pp. 161-187, (2000).         [ Links ]

[7] Gulisashvili, A. and Kon, M., Exact smoothing properties of Schrödinger semigoups, Amer. J. Math. 118, pp. 1215-1248, (1996).         [ Links ]

[8] Simon, B., Schrödinger semigroups, Bull. Amer. Math. Soc. 7, pp. 445-526, (1982).         [ Links ]

[9] Stein, E., Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, (1970).         [ Links ]

[10] Zamboni, P., Unique continuation for non-negative solutions of quasi-linear elliptic equations, Bull. Austral. Math. Soc. 64, pp. 149-156, (2001).         [ Links ]


René Erlín Castillo

Departamento de Matemáticas, Universidad Nacional de Colombia, Ciudad Universitaria: Carrera 30, Calle 45, Bogotá, Colombia

e-mail :

Received: January 2011. Accepted : November 2011

Creative Commons License