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Mean inequalities in certain Banach function spaces

2007; Elsevier BV; Volume: 334; Issue: 1 Linguagem: Inglês

10.1016/j.jmaa.2006.12.061

1096-0813

Pankaj Jain, Babita Gupta, Daulti Verma,

Holomorphic and Operator Theory

Boundedness of the Hardy operator ( H f ) ( x ) = ∫ 0 x f ( t ) d t and its adjoint ( H ∗ f ) ( x ) = ∫ x ∞ f ( t ) d t is characterized between Banach function spaces X q and L p . By applying a limiting procedure, corresponding boundedness of the geometric mean operator ( G f ) ( x ) = exp ( 1 x ∫ 0 x ln f ( t ) d t ) is also derived.