Weighted integral inequalities with the geometric mean operator
نویسندگان
چکیده
منابع مشابه
Some weighted operator geometric mean inequalities
In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
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We consider T f = ∫ x1 0 ∫ x2 0 f (t1, t2)dt1dt2 and a corresponding geometric mean operator G f = exp(1/x1x2) ∫ x1 0 ∫ x2 0 log f (t1, t2)dt1dt2. E. T. Sawyer showed that the Hardy-type inequality ‖T f ‖Lq u ≤ C‖ f ‖Lp v could be characterized by three independent conditions on the weights. We give a simple proof of the fact that if the weight v is of product type, then in fact only one condit...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2002
ISSN: 1029-242X
DOI: 10.1155/s1025583402000371