The Orlicz Inequality for Series of Multilinear Forms
Salih Yousuf Mohamed Salih *
Department of Mathematics, College of Science, University of Bakht Al-Ruda, Sudan.
Shawgy Hussein
Department of Math, College of Science, Sudan University of Science and Technology, Sudan.
*Author to whom correspondence should be addressed.
Abstract
The Orlicz ( \(\ell\)2,\(\ell\)1)-mixed inequality of integers and fractional dimensions who states that, with a bit of extend,
for all sequences of bilinear forms AL: \(\mathbb{K}\)n x \(\mathbb{K}\)n \(\rightarrow\) \(\mathbb{K}\) and all positive integers n, where \(\mathbb{K}\)n denotes \(\mathbb{R}\)n or \(\mathbb{C}\)n endowed with the supremum norm. For that we follow D.Núñez-Alarcón, D. Pellegrino, and D. Serrano-Rodríguez [1]] to extend this inequality to series of multilinear forms, with \(\mathbb{K}\)n endowed with \(\ell\)1+ \(\epsilon\) norms for all successive gradually of the general 0 ≤ ϵ ≤ ∞.
Keywords: Orlicz inequality, multilinear forms, hölder inequality, hardy-littlewood inequalities, maurey-pisier factorization