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Reiteration of a limiting real interpolation method with broken iterated logarithmic functions

Year 2019, Volume: 48 Issue: 4, 966 - 972, 08.08.2019

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

  • [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.
Year 2019, Volume: 48 Issue: 4, 966 - 972, 08.08.2019

Abstract

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.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

İrshaad Ahmed This is me 0000-0003-0630-7620

Fakhra Umar This is me 0000-0003-0289-5891

Publication Date August 8, 2019
Published in Issue Year 2019 Volume: 48 Issue: 4

Cite

APA Ahmed, İ., & Umar, F. (2019). Reiteration of a limiting real interpolation method with broken iterated logarithmic functions. Hacettepe Journal of Mathematics and Statistics, 48(4), 966-972.
AMA Ahmed İ, Umar F. Reiteration of a limiting real interpolation method with broken iterated logarithmic functions. Hacettepe Journal of Mathematics and Statistics. August 2019;48(4):966-972.
Chicago Ahmed, İrshaad, and Fakhra Umar. “Reiteration of a Limiting Real Interpolation Method With Broken Iterated Logarithmic Functions”. Hacettepe Journal of Mathematics and Statistics 48, no. 4 (August 2019): 966-72.
EndNote Ahmed İ, Umar F (August 1, 2019) Reiteration of a limiting real interpolation method with broken iterated logarithmic functions. Hacettepe Journal of Mathematics and Statistics 48 4 966–972.
IEEE İ. Ahmed and F. Umar, “Reiteration of a limiting real interpolation method with broken iterated logarithmic functions”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 4, pp. 966–972, 2019.
ISNAD Ahmed, İrshaad - Umar, Fakhra. “Reiteration of a Limiting Real Interpolation Method With Broken Iterated Logarithmic Functions”. Hacettepe Journal of Mathematics and Statistics 48/4 (August 2019), 966-972.
JAMA Ahmed İ, Umar F. Reiteration of a limiting real interpolation method with broken iterated logarithmic functions. Hacettepe Journal of Mathematics and Statistics. 2019;48:966–972.
MLA Ahmed, İrshaad and Fakhra Umar. “Reiteration of a Limiting Real Interpolation Method With Broken Iterated Logarithmic Functions”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 4, 2019, pp. 966-72.
Vancouver Ahmed İ, Umar F. Reiteration of a limiting real interpolation method with broken iterated logarithmic functions. Hacettepe Journal of Mathematics and Statistics. 2019;48(4):966-72.