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A characterization for the boundedness of geometric mean operator

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Publication Date
Volume
13
Issue
8
Identifiers
DOI: 10.1016/s0893-9659(00)00097-5
Keywords
  • Inequalities
  • Geometric Mean Inequality
  • Geometric Mean Operator
  • Averaging Operator
Disciplines
  • Mathematics

Abstract

Abstract We give a characterization for the geometric mean inequality ∫ 0 ∞ exp κ+1 x κ+1 ∫ 0 x + k lnf(+)dt qu(x) 1 q ⩽c ∫ 0 ∞ f p(x)v(x)dx 1 p to hold for the case 0 < q < p ≤ ∞, p > 1, where f is positive a.e. on (0, ∞), and C > 0 independent of f.

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