Weighted inequalities for geometric means
1994; American Mathematical Society; Volume: 120; Issue: 3 Linguagem: Inglês
10.1090/s0002-9939-1994-1169043-4
ISSN1088-6826
Autores Tópico(s)Functional Equations Stability Results
ResumoA characterization of weights u , v u,v is given for which the geometric mean operator T f ( x ) = exp ( 1 x ∫ 0 x ln f ( t ) d t ) Tf(x) = \exp (\tfrac {1} {x}\int _0^x {\ln \;f(t)\,dt)} , defined for f f positive a.e. on ( 0 , ∞ ) (0,\infty ) , is bounded from L p ( ( 0 , ∞ ) ; v d x ) {L^p}((0,\infty );v\,dx) to L q ( ( 0 , ∞ ) ; u d x ) , p ∈ ( 0 , ∞ ) {L^q}((0,\infty );u\,dx),p \in (0,\infty ) and q ∈ [ p , ∞ ) q \in [p,\infty ) .
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