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On Weighted Norm Inequalities with Three Weights
Author(s) -
Oinarov R.
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-48.1.103
Subject(s) - norm (philosophy) , mathematics , compact space , combinatorics , inequality , characterization (materials science) , discrete mathematics , pure mathematics , physics , mathematical analysis , political science , optics , law
A characterization is given of the weights r, p, v when the weighted norm inequality(∫ a b| r f |q )1 / q ⩽ C(∫ a b| p f ′ |q +∫ a b| v f |p )1 / pholds. Both cases 1 ⩽ p ⩽ q ⩽ ∞ and 1 ⩽ q < p ⩽ ∞ are considered and the related problems of compactness are also studied.