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    Barza, S. Marcoci, A. N. and Persson, L. E. 2012. Best Constants between Equivalent Norms in Lorentz Sequence Spaces. Journal of Function Spaces and Applications, Vol. 2012, Issue. , p. 1.
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SHARP CONSTANTS BETWEEN EQUIVALENT NORMS IN WEIGHTED LORENTZ SPACES

  • SORINA BARZA (a1) and JAVIER SORIA (a2)
Abstract

For an increasing weight w in Bp (or equivalently in Ap), we find the best constants for the inequalities relating the standard norm in the weighted Lorentz space Λp(w) and the dual norm.

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Copyright
COPYRIGHT: © Australian Mathematical Publishing Association Inc. 2010
Corresponding author
✉For correspondence; e-mail: soria@ub.edu
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This research was partially supported by grants MTM2007-60500 and 2005SGR00556.

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References
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[1]Ariño, M. A. and Muckenhoupt, B., ‘Maximal functions on classical Lorentz spaces and Hardy’s inequality with weights for nonincreasing functions’, Trans. Amer. Math. Soc. 320 (1990), 727–735.
[2]Barza, S., Kolyada, V. and Soria, J., ‘Sharp constants related to the triangle inequality in Lorentz spaces’, Trans. Amer. Math. Soc. 361 (2009), 5555–5574.
[3]Bennett, C. and Sharpley, R., Interpolation of Operators (Academic Press, New York, 1988).
[4]Carro, M. J., Pick, L., Soria, J. and Stepanov, V. D., ‘On embeddings between classical Lorentz spaces’, Math. Inequal. Appl. 4 (2001), 397–428.
[5]Carro, M. J., Raposo, J. A. and Soria, J., Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities, Memoirs of the American Mathematical Society, 187 (American Mathematical Society, Providence, RI, 2007).
[6]Carro, M. J. and Soria, J., ‘Weighted Lorentz spaces and the Hardy operator’, J. Funct. Anal. 112 (1993), 480–494.
[7]Cerdà, J. and Martín, J., ‘Weighted Hardy inequalities and Hardy transforms of weights’, Studia Math. 139 (2000), 189–196.
[8]Halperin, I., ‘Function spaces’, Canad. J. Math. 5 (1953), 273–288.
[9]Hardy, G. H., Littlewood, J. E. and Pólya, G., Inequalities, 2nd edn (Cambridge University Press, Cambridge, 1952).
[10]Kamińska, A. and Parrish, A. M., ‘Convexity and concavity constants in Lorentz and Marcinkiewicz spaces’, J. Math. Anal. Appl. 343 (2008), 337–351.
[11]Korenovskiĭ, A. A., ‘The exact continuation of a reverse Hölder inequality and Muckenhoupt’s condition’, Mat. Zametki 52(6) (1992), 32–44 (Engl. Transl. Math. Notes 52(5–6) (1992), 1192–1201).
[12]Lorentz, G. G., ‘Some new functional spaces’, Ann. of Math. (2) 51 (1950), 37–55.
[13]Lorentz, G. G., ‘On the theory of spaces Λ’, Pacific J. Math. 1 (1951), 411–429.
[14]Muckenhoupt, B., ‘Weighted norm inequalities for the Hardy maximal function’, Trans. Amer. Math. Soc. 165 (1972), 207–227.
[15]Sawyer, E., ‘Boundedness of classical operators on classical Lorentz spaces’, Studia Math. 96 (1990), 145–158.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
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