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Integral Operators on the Cone of Monotone Functions
Author(s) -
Stepanov Vladimir D.
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/s2-48.3.465
Subject(s) - mathematics , monotone polygon , cone (formal languages) , bounded function , pure mathematics , operator (biology) , lorentz space , linear operators , lorentz transformation , operator theory , mathematical analysis , space (punctuation) , hardy space , physics , geometry , biochemistry , chemistry , algorithm , repressor , classical mechanics , transcription factor , gene , linguistics , philosophy
Necessary and sufficient conditions for the boundedness of linear integral operators fromL U P ( R + ) toL Q W ( R + ) restricted to the cones of monotone functions are given. In addition a general approach to a number of classical operators is explicitly described. In particular, we determine when the Hardy‐Littlewood maximal operator is bounded in the classical Lorentz space Γ p (v) consisting of those measurable functions on R n such that(∫ 0 ∞ f ∗ ∗ ( t ) p υ ( t ) d t)1 / p < ∞ .