Propiedades de aproximación en espacios de Herz

  • Jhean E. Pérez-López Universidad Industrial de Santander


In this paper we consider the Herz spaces Kαp,q , which are a natural generalization of the Lebesgue spaces Lp . We prove some approximation properties such as density of the space C∞ c (R n), continuity of the translation, continuity of the mollification, global behavior of the convolution with smooth funtions, among others.

Palabras clave: Espacios de Herz, Molificadores, Convolución, Espacios funcionales


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Biografía del autor/a

Jhean E. Pérez-López, Universidad Industrial de Santander

Escuela de Matemáticas, Bucaramanga, Colombia.


[1] Chen Y.Z. and Lau K.S., "On some new classes of Hardy spaces", J. Funct. Anal. 84 (1989), 255-278.

[2] DiPerna R.J. and Lions P.L., "Ordinary differential equations, transport theory and Sobolev spaces", Invent. Math. 98 (1989), No. 3, 511-547.

[3] Ferreira L.C.F. and Pérez-López J.E., "On the theory of Besov-Herz spaces and Euler equations", Israel J. Math. 220 (2017), No. 1, 283-332.

[4] García-Cuerva J. and Herrero M.-J.L., "A theory of Hardy spaces associated to the Herz spaces", Proc. Lond. Math. Soc. (3) 69 (1994), No. 3, 605-628.

[5] Grafakos L., Li X. and Yang D., "Bilinear Operators on Herz-type Hardy spaces", Trans. Amer. Math. Soc. 350 (1998), No. 3, 1249-1275.

[6] Hernandez E. and Yang D., "Interpolation of Herz spaces and applications", Math. Nachr. 205 (1999), No.1, 69-87.

[7] Herz C.S., "Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transforms", J. Math. Mech. 18 (1968/69), 283-323.

[8] Johnson R., "Lipschitz spaces, Littlewood-Paley spaces, and convoluteurs", Proc. Lond. Math. Soc. (3) 29 (1974), No. 1, 127-141.

[9] Tsutsui Y., "The Navier-Stokes equations and weak Herz spaces", Adv. Differential Equations 16 (2011), No. 11-12, 1049-1085.

[10] Xu J., "Equivalent norms of Herz-type Besov and Triebel-Lizorkin spaces", J. Funct. Spaces Appl. 3 (2005), No. 1, 17-31.