Reiteration of a limiting real interpolation method with broken iterated logarithmic functions
Year 2019,
Volume: 48 Issue: 4, 966 - 972, 08.08.2019
İrshaad Ahmed
Fakhra Umar
Abstract
A reiteration theorem for a limiting real interpolation method with broken iterated logarithmic functions is established. An application to the generalized Lorentz-Zygmund spaces is given.
References
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slowly varying functions, Q. J. Math. 63 (1), 133-164, 2012.
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parameters, Ark. Mat. 52 (2), 227-256, 2014.
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Nachr. 288 (1), 25-47, 2015.
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62 (3), 929-948, 2016.
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Inequal. Appl. 19 (2), 597-624, 2016.
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with slowly varying functions, Math. Nachr. 278 (1-2) 86-107, 2005.
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Studia Math. 116 (2), 133-165, 1995.
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Holland, Amsterdam, 1978.
Year 2019,
Volume: 48 Issue: 4, 966 - 972, 08.08.2019
İrshaad Ahmed
Fakhra Umar
References
- [1] I. Ahmed, D.E. Edmunds, W.D. Evans and G.E. Karadzhov, Reiteration theorems for
the K-interpolation method in limiting cases, Math. Nachr. 284 (4), 421-442, 2011.
- [2] I. Ahmed, G.E. Karadzhov and A. Raza, General Holmstedt’s formulae for the K-
functional, J. Funct. Spaces 2017, Article ID 4958073, 9 pages, 2017.
- [3] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, New York,
1988.
- [4] J. Bergh and J. Löfström, Interpolation spaces. An introduction, Springer-Verlag, New
York, 1976.
- [5] F. Cobos and T. Kühn, Equivalence of K- and J-methods for limiting real interpolation
spaces, J. Funct. Anal. 261 (12), 3696-3722, 2011.
- [6] R.Ya. Doktorski, Limiting reiteration for real interpolation with logarithmic functions,
Bol. Soc. Mat. Mex. 22 (2), 679-693, 2016.
- [7] D.E. Edmunds and W.D. Evans, Hardy operators, function spaces and embeddings,
Springer, Berlin-Heidelberg-New York, 2004.
- [8] W.D. Evans and B. Opic, Real interpolation with logarithmic functors and reiteration,
Canad. J. Math. 52 (5), 920-960, 2000.
- [9] W.D. Evans, B. Opic and L. Pick, Real interpolation with logarithmic functors, J.
Inequal. Appl. 7 (2), 187-269, 2002.
- [10] P. Fernández-Martínez, A. Segurado and T. Signes, Compactness results for a class
of limiting interpolation methods, Mediterr. J. Math. 13 (5), 2959-2979, 2016.
- [11] P. Fernández-Martínez and T. Signes, Real interpolation with symmetric spaces and
slowly varying functions, Q. J. Math. 63 (1), 133-164, 2012.
- [12] P. Fernández-Martínez and T. Signes, Reiteration theorems with extreme values of
parameters, Ark. Mat. 52 (2), 227-256, 2014.
- [13] P. Fernández-Martínez and T. Signes, Limit cases of reiteration theorems, Math.
Nachr. 288 (1), 25-47, 2015.
- [14] P. Fernández-Martínez and T. Signes, A limiting case of ultrasymmetric spaces, Mathematika
62 (3), 929-948, 2016.
- [15] P. Fernández-Martínez and T. Signes, Limiting ultrasymmetric sequence spaces, Math.
Inequal. Appl. 19 (2), 597-624, 2016.
- [16] A. Gogatishvili, B. Opic and W. Trebels, Limiting reiteration for real interpolation
with slowly varying functions, Math. Nachr. 278 (1-2) 86-107, 2005.
- [17] H. Heinig and L. Maligranda, Weighted inequalities for monotone and concave functions,
Studia Math. 116 (2), 133-165, 1995.
- [18] H. Triebel, Interpolation theory, function spaces, differential operators, North-
Holland, Amsterdam, 1978.