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Elementary reverse Hölder type inequalities with application to operator interpolation theory
Author(s):
Jesús
Bastero;
Francisco
J.
Ruiz
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3183-3192.
MSC (1991):
Primary 46E30, 46B70
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Abstract:
We give a very elementary proof of the reverse Hölder type inequality for the classes of weights which characterize the boundedness on  of the Hardy operator for nonincreasing functions. The same technique is applied to Calderón operator involved in the theory of interpolation for general Lorentz spaces. This allows us to obtain further consequences for intermediate interpolation spaces.
References:
- [AM]
- M.A. Ariño and B. Muckenhoupt, Maximal Functions on Classical Lorentz Spaces and Hardy's Inequality with Weights for Nonincreasing Functions, Transactions A.M.S. 320 (2) (1990), 727--735. MR 90k:42034
- [BL]
- J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag, New York, 1976. MR 58:2349
- [BS]
- C. Bennett and R. Sharpley, Interpolation of operators, Academic Press, 1988. MR 89e:46001
- [BR]
- J. Bastero and F. Ruiz, Interpolation of operators when the extreme spaces are
 , Studia Math. 104 (2) (1993), 133--150. MR 94g:46087 - [C]
- M. Cwikel,
 -divisibility of the  -functional and Calderón couples, Arkiv för matematik 22 (1) (1984), 39--62. MR 85m:46074 - [DK]
- V. Dmitriev and S.G. Krein, Interpolation of operators of weak type, Analysis Mathematica 4 (1978), 83--99. MR 80h:46036
- [K]
- N. Kalton, Calderón couples of rearrangement invariant spaces, Studia Mathematica 106 (3) (1993), 233--277. MR 94k:46152
- [L]
- G.G. Lorentz, Majorants in spaces of integrable functions, Amer. J. Math. 77 (1955), 484--492. MR 17:65a
- [LT]
- J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer Verlag, 1979. MR 81c:46001
- [M]
- B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207--226. MR 45:2461
- [Ma1]
- L. Maligranda, Indices and interpolation, Dissertationes Math. 234 (1985). MR 87k:46059
- [Ma2]
- ------, The
 -functional for symmetric spaces, Lecture Notes in Mathematics Springer 1070 (1984), 169--182. MR 86d:46026 - [N]
- C. J. Neugebauer, Weighted norm inequalities for averaging operators of monotone functions, Publications Matematiques 35 (1991), 429--447. MR 93m:26042
- [R]
- Y. Raynaud, On Lorentz-Sharpley spaces, Proceedings of the Workshop Interpolation Spaces and Related Topics", Haifa, 1990. MR 94c:46061
- [S]
- E. Sawyer, Boundedness of Classical Operators on Classical Lorentz Spaces, Studia Math. 96 (1990), 145--158. MR 91d:26026
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Additional Information:
Jesús
Bastero
Affiliation:
Department of Mathematics, University of Zaragoza, 50009-Zaragoza, Spain
Email:
bastero@posta.unizar.es
Francisco
J.
Ruiz
Affiliation:
Department of Mathematics, University of Zaragoza, 50009-Zaragoza, Spain
Email:
fjruiz@posta.unizar.es
DOI:
10.1090/S0002-9939-96-03651-9
PII:
S 0002-9939(96)03651-9
Keywords:
Hardy operator,
weighted norm inequalities,
Lorentz spaces,
interpolation of operators
Received by editor(s):
May 22, 1993
Received by editor(s) in revised form:
April 10, 1995
Additional Notes:
The first author was partially supported by DGICYT PS90-012
The second author was partially supported by DGICYT PS89-0181 and DGICYT PS93-0228-C02-02.
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1996,
American Mathematical Society
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