Summation of coefficients of polynomials on lp-spaces

• Autores: Dimant, Veronica Isabel; Sevilla Peris, Pablo
• Año de publicación: 2016
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Homogeneous polynomials; Multilinear mappings; Sequence spaces; Hardy-LLittlewood inequalities
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina
Fil: Sevilla Peris, Pablo. Universidad Politécnica de Valencia; España