schur test
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2005 ◽  
Vol 31 (4) ◽  
pp. 277-289 ◽  
Author(s):  
Salti Samarah ◽  
S. Obeidat ◽  
R. Salman


2005 ◽  
Vol 57 (5) ◽  
pp. 897-940 ◽  
Author(s):  
Evgenii I. Berezhnoĭ ◽  
Lech Maligranda

AbstractRepresentation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calderón–Lozanovskiĭ construction. Factorization theorems for operators in spaces more general than the Lebesgue Lpspaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de Francia theorem on factorization of the Muckenhoupt Ap weights to reflexive Orlicz spaces. However, it turns out that for the scales far fromLp-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calderón–Lozanovskiĭ construction are involved in the proofs.



2001 ◽  
Vol 187 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Loukas Grafakos ◽  
Rodolfo H. Torres


1998 ◽  
Vol 160 (2) ◽  
pp. 543-560 ◽  
Author(s):  
J.F Toland ◽  
D Williams


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