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Inequalities and interpolation.

L. Maligranda;  L. E. Persson — 1993

Collectanea Mathematica

Some examples of the close interaction between inequalities and interpolation are presented and discussed. An interpolation technique to prove generalized Clarkson inequalities is pointed out. We also discuss and apply to the theory of interpolation the recently found facts that the Gustavsson-Peetre class P can be described by one Carlson type inequality and that the wider class P can be characterized by another Carlson type inequality with blocks.

Schur multiplier characterization of a class of infinite matrices

A. Marcoci;  L. Marcoci;  L. E. Persson;  N. Popa — 2010

Czechoslovak Mathematical Journal

Let B w ( ℓ p ) denote the space of infinite matrices A for which A ( x ) ∈ ℓ p for all x = { x k } k = 1 ∞ ∈ ℓ p with | x k | ↘ 0 . We characterize the upper triangular positive matrices from B w ( ℓ p ) , 1 < p < ∞ , by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.

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