Summation of coefficients of polynomials on lp-spaces

We investigate the summability of the coefficients of $m$-homogeneous polynomials and $m$-linear mappings defined on $\ell_{p}$-spaces. In our research we obtain resultson the summability of the coefficients of $m$-linear mappings defined on $\ell_{p_{1}} \times \cdots \times \ell_{p_{m}}$. The firs...

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Detalles Bibliográficos
Autores: Dimant, Veronica Isabel, Sevilla Peris, Pablo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/46724
Acceso en línea:http://hdl.handle.net/11336/46724
Access Level:acceso abierto
Palabra clave:Homogeneous polynomials
Multilinear mappings
Sequence spaces
Hardy-LLittlewood inequalities
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We investigate the summability of the coefficients of $m$-homogeneous polynomials and $m$-linear mappings defined on $\ell_{p}$-spaces. In our research we obtain resultson the summability of the coefficients of $m$-linear mappings defined on $\ell_{p_{1}} \times \cdots \times \ell_{p_{m}}$. The first results in this respect go back to Littlewood andBohnenblust and Hille (for bilinear and $m$-linear forms on $c_{0}$) and Hardy and Littlewood and Praciano-Pereira (for bilinear and $m$-linear forms on arbitrary $\ell_{p}$-spaces).Our results recover and in some case complete these old results through a general approach on vector valued $m$-linear mappings.