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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.26 n.1 San José Jan./Jun. 2019 


Characterization of bmo using wavelets through triebellizorkin spaces

Caracterización de bmo usando ondículas por medio del espacio de triebel-lizorkin

Jorge Eliécer  Hernández Hernández1 

1Departamento de Técnicas Cuantitativas, Decanato de Ciencias Económicas y Empresa- riales, Universidad Centroccidental Lisandro Alvarado. Barquisimeto, Venezuela. E-Mail:



In the present article it is presented a characterization of all those func- tions in the space of bounded mean oscillation functions, BM O, in terms of an appropriate wavelet, using an isomorphism between the aforemen- tioned space and the homogeneous space of Triebel-Lizorkin F˙ 0,2. In ad- dition, a new inequality that involves the vector inequality of the maximal function of Hardy-Littlewood is proved.

Keywords: BMO function space; Triebel-Lizorkin’s homogeneous space; wavelets



En el presente artículo se presenta una caracterización de todas aque- llas funciones pertenecientes al espacio de oscilación media acotada, BM O, en términos de una apropiada ondícula, usando un isomorfismo entre el mencionado espacio de funciones y el espacio homogéneo de Triebel-Lizorkin F˙ 0,2. Además, se prueba una versión nueva que involucra la desigualdad v∞ectorial de la función maximal de Hardy-Littlewood.

Palabras clave: espacio de funciones de oscilación media acotada; espacio homogéneo de Triebel-Lizorkin; ondículas

Mathematics Subject Classification: Primary 22E46, 53C35, Secondary 57S20.


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The author thanks to the Council for Scientific, Humanistic and Technological Development (CDCHT) of Universidad Centroccidental Lisandro Alvarado, and especially to Dr. Ventura Echandía Dean of the School of Sciences of the Fac- ulty of Sciences of the Central University of Venezuela for his teachings and contributions.


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Received: November 09, 2017; Revised: June 02, 2018; Accepted: November 07, 2018

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