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Interpolation of real method spaces via some ideals of operators

100%

Mastyło M., Milman M.

Studia Mathematica

1999

tom 136

nr 1

17-35

Certain operator ideals are used to study interpolation of operators between spaces generated by the real method. Using orbital equivalence a new reiteration formula is proved for certain real interpolation spaces generated by ordered pairs of Banach lattices of the form $(X,L_∞(w))$. As an application we extend Ovchinnikov's interpolation theorem from the context of classical Lions-Peetre spaces to a larger class of real interpolation spaces. A description of certain abstract J-method spaces is also presented.

On sharp reiteration theorems and weighted norm inequalities

81%

Bastero J., Milman M., Ruiz F. J.

Studia Mathematica

2000

tom 142

nr 1

7-24

We prove sharp end forms of Holmstedt's reiteration theorem which are closely connected with a general form of Gehring's Lemma. Reverse type conditions for the Hardy-Littlewood-Pólya order are considered and the maximal elements are shown to satisfy generalized Gehring conditions. The methods we use are elementary and based on variants of reverse Hardy inequalities for monotone functions.

Ograniczanie wyników

2 Studia Mathematica

2 Milman M.

1 Bastero J.

1 Mastyło M.

1 Ruiz F. J.

1 2000

1 1999

Wyniki wyszukiwania

Interpolation of real method spaces via some ideals of operators

On sharp reiteration theorems and weighted norm inequalities