Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Lorentz-Karamata spaces; equivalent quasi-norms; weighted norm inequalities; fractional maximal operators; Riesz potentials
Lorentz-Karamata spaces; equivalent quasi-norms; weighted norm inequalities; fractional maximal operators; Riesz potentials
Summary:
References:
[1] C. Bennett and K. Rudnick: On Lorentz-Zygmund spaces. Dissertationes Math. 175 (1980), 1–72. MR 0576995
[2] C. Bennett and R. Sharpley: Interpolation of operators. Academic Press, New York, 1988. MR 0928802
[3] N. H. Bingham, C. M. Goldie and J. L. Teugels: Regular variation. Cambridge Univ. Press, Cambridge, 1987. MR 0898871
[4] A. P. Calderón: Spaces between $L^1$ and $L^{\infty }$ and the theorem of Marcinkiewicz. Studia Math. 26 (1966), 273–299. MR 0203444
[5] D. E. Edmunds and W. D. Evans: Hardy operators, function spaces and embeddings. Springer-Verlag, Berlin-Heidelberg, 2004. MR 2091115
[6] D. E. Edmunds, P. Gurka and B. Opic: Double exponential integrability of convolution operators in generalised Lorentz-Zygmund spaces. Indiana Univ. Math. J. 44 (1995), 19–43. MR 1336431
[7] D. E. Edmunds, P. Gurka and B. Opic: On embeddings of logarithmic Bessel potential spaces. J. Functional Anal. 146 (1997), 116–150. MR 1446377
[8] D. E. Edmunds and B. Opic: Boundedness of fractional maximal operators between classical and weak-type Lorentz spaces. Dissertationes Math. 410 (2002), 1–53. MR 1952673
[9] D. E. Edmunds and B. Opic: Equivalent quasi-norms on Lorentz spaces. Proc. Amer. Math. Soc. 131 (2003), 745–754. MR 1937412
[10] W. D. Evans and B. Opic: Real interpolation with logarithmic functors and reiteration. Canad. J. Math. 52 (2000), 920–960. MR 1782334
[11] A. Gogatishvili, B. Opic and W. Trebels: Limiting reiteration for real interpolation with slowly varying functions. Math. Nachr. 278 (2005), 86–107. MR 2111802
[12] S. Lai: Weighted norm inequalities for general operators on monotone functions. Trans. Amer. Math. Soc. 340 (1993), 811–836. MR 1132877 | Zbl 0819.47044
[13] J. S. Neves: Lorentz-Karamata spaces, Bessel and Riesz potentials and embeddings. Dissertationes Math. 405 (2002), 1–46. MR 1927106 | Zbl 1017.46021
[14] B. Opic: New characterizations of Lorentz spaces. Proc. Royal Soc. Edinburgh 133A (2003), 439–448. MR 1969821 | Zbl 1037.46026
[15] B. Opic: On equivalent quasi-norms on Lorentz spaces. In Function Spaces, Differential Operators and Nonlinear Analysis. The Hans Triebel Aniversary Volume, D. Haroske, T. Runst, H.-J. Schmeisser (eds.), Birkhäuser Verlag, Basel/Switzerland, 2003, pp. 415–426. MR 1984189 | Zbl 1036.46022
[16] B. Opic and W. Trebels: Sharp embeddings of Bessel potential spaces with logarithmic smoothness. Math. Proc. Camb. Phil. Soc. 134 (2003), 347–384. MR 1972143
Search
Partner of
