New results for generalized Hausdorff matrices

• Published in: Journal of inequalities and applications Vol. 2025; no. 1; pp. 100 - 7
• Main Author: Talebi, Gholamreza
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2025; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Generalized Hausdorff matrix; Inequality; Linear algebra; Lower bound; Mathematics; Mathematics and Statistics; Theorems; Lower bound; 40G05; Generalized Hausdorff matrix; 46A45
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-025-03354-y

Let A = ( a n , k ) n , k ≥ 0 be a non-negative matrix. Denote by L p ( A ) , the supremum of those  ℓ , satisfying the following inequality ( ∑ n = 0 ∞ ( ∑ k = 0 ∞ a n , k x k ) p ) 1 p ≥ ℓ ( ∑ k = 0 ∞ x k p ) 1 p ( x ≥ 0 , x ∈ ℓ p ) . In this paper, we establish the exact value of L p ( ( H μ s ) t ) , where H μ s is the generalized Hausdorff matrix and 0 < p ≤ 1 . We also establish a similar result for L p ( H μ s ) with − ∞ < p < 0 . Main results of the paper fill up the gaps which the recent works of Chen and Wang have not dealt with.