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Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations

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Abstract

The real interpolation method is considered and it is proved that for general local Morrey-type spaces, in the case in which they have the same integrability parameter, the interpolation spaces are again general local Morrey-type spaces with appropriately chosen parameters. This result is a particular case of the interpolation theorem for much more general spaces defined with the help of an operator acting from some function space to the cone of nonnegative nondecreasing functions on (0, ∞). It is also shown how the classical interpolation theorems due to Stein-Weiss, Peetre, Calderón, Gilbert, Lizorkin, Freitag and some of their new variants can be derived from this theorem.

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Authors and Affiliations

  1. School of Mathematics, Cardiff University, Senghennydd Road, CF24 4AG, Cardiff, Wales, UK

    V. I. Burenkov

  2. L.N. Gumilyov Eurasian National University, Mirzoyana str. 2, Astana, 010008, Kazakhstan

    V. I. Burenkov, E. D. Nursultanov & D. K. Chigambayeva

  3. Kazakhstan Branch of the Moscow State University, Kazhimukana str. 11, Astana, 010010, Kazakhstan

    E. D. Nursultanov

Authors
  1. V. I. Burenkov
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  2. E. D. Nursultanov
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  3. D. K. Chigambayeva
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Correspondence to V. I. Burenkov.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Vol. 284, pp. 105–137.

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Burenkov, V.I., Nursultanov, E.D. & Chigambayeva, D.K. Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations. Proc. Steklov Inst. Math. 284, 97–128 (2014). https://doi.org/10.1134/S0081543814010064

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  • DOI: https://doi.org/10.1134/S0081543814010064

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