On the Multi-Dimensional Duality Principle of Sawyer Type
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Abstract
A multi-dimensional version of the duality principle of Sawyer type [1] is obtained whenever the corresponding weight satisfies some doubling property.
Keywords
Multi-dimensional duality principle Doubling weights Weighted inequalities Decreasing functionsMR (1991) Subject Classification
26D15Preview
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References
- 1.E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia. Math., 1990, 96:149–158MathSciNetGoogle Scholar
- 2.S. Barza, L. E. Persson, H. Heinig, Duality theorem over the cone of monotone functions of several variables, Preprint, Lulea University of Technology, Sweden, 1999, in pressGoogle Scholar
- 3.S. Barza, L. E. Persson, V. Stepanov, On weighted multi-dimensional embeddings for monotone functions, Math. Scand., 1998, 19:30Google Scholar
- 4.S. Barza, Weighted multi-dimensional integral inequalities and applications, Doctoral Thesis, Lulea University of Technology, Sweden, 1999, 30 (ISSN: 1402–1544). Google Scholar
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© Springer-Verlag Berlin Heidelberg 2001