Relative rearrangement on a finite measure space. Application to weighted spaces and to P.D.E.
Jean Michel Rakotoson, Benoît Simon (1997)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Jean Michel Rakotoson, Benoît Simon (1997)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Gord Sinnamon (2003)
Collectanea Mathematica
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Certain weighted norm inequalities for integral operators with non-negative, monotone kernels are shown to remain valid when the weight is replaced by a monotone majorant or minorant of the original weight. A similar result holds for operators with quasi-concave kernels. To prove these results a careful investigation of the functional properties of the monotone envelopes of a non-negative function is carried-out. Applications are made to function space embeddings of the cones of monotone...
Gonoko Moussa (1998)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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H. Beirão Da Veiga (1976)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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J. Michel Rakotoson (2003)
RACSAM
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We prove here that the Poincaré-Sobolev pointwise inequalities for the relative rearrangement can be considered as the root of a great number of inequalities in various sets not necessarily vector spaces. In particular, new interpolation inequalities can be derived.
Gord Sinnamon (1994)
Studia Mathematica
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The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of . These domains are shown to be Banach spaces which, although closely tied to spaces, are not reflexive. A related construction is given which characterizes their dual spaces.
J. Mossino, J. M. Rakotoson (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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G. R. Burton (1989)
Annales de l'I.H.P. Analyse non linéaire
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