Artículos científicos
Publicado 2018-03-06
Palabras clave
- Espacios de Herz,
- Molificadores,
- Convolución,
- Espacios funcionales
Cómo citar
Pérez-López, J. E. (2018). Propiedades de aproximación en espacios de Herz. Revista Integración, Temas De matemáticas, 35(2), 215–223. https://doi.org/10.18273/revint.v35n2-2017005
Derechos de autor 2019 Revista Integración, temas de matemáticas
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
Resumen
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.
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Referencias
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[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.
[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.