Research and Innovation Articles
Published 2018-03-06
Keywords
- Herz spaces,
- Mollifiers,
- convolution,
- funtional spaces
How to Cite
Pérez-López, J. E. (2018). Approximation properties on Herz spaces. Revista Integración, Temas De matemáticas, 35(2), 215–223. https://doi.org/10.18273/revint.v35n2-2017005
Copyright (c) 2019 Revista Integración, temas de matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
En este artículo consideramos los espacios de Herz Kαp,q , los cuales son una generalización natural de los espacios de Lebesgue Lp . Demostramos algunas propiedades de aproximación tales como densidad del espacio C∞ c (R n), continuidad de la traslación, continuidad de la molificación, comportamiento global de la convolución con funciones suaves, entre otras.
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References
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[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.