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Morrey-Campanato Spaces: an Overview

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Book cover Operator Theory, Pseudo-Differential Equations, and Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 228))

Abstract

In this paper we overview known and recently obtained results on Morrey-Campanato spaces with respect to the properties of the spaces themselves, that is, we do not touch the study of operators in these spaces. In particular, we overview equivalent definitions of various versions of the spaces, the so-called ϕ- and θ-generalizations, structure of the spaces, embeddings, dual spaces, etc.

Mathematics Subject Classification (2010). Primary 46E30; Secondary 46E35.

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  1. Instituto Superior Técnico, Centro CEAF, Av. Rovisco Pais, 1049–001, Lisboa, Portugal

    Humberto Rafeiro

  2. Universidade do Algarve, Campus de Gambelas, 8005–139, Faro, Portugal

    Natasha Samko & Stefan Samko

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  1. Humberto Rafeiro
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  2. Natasha Samko
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Correspondence to Humberto Rafeiro .

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  1. de Morelos, Facultad de Ciencias, Universidad Autónoma del Estado, Av. Universidad 1001, Col. Chamilpa, Cuernavaca, 62209, Morelos, Mexico

    Yuri I. Karlovich

  2. , Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, Torino, 10123, Italy

    Luigi Rodino

  3. , Fakultät für Mathematik, Technische Universität Chemnitz, Reichenhainer Straße 39, Chemnitz, 09126, Germany

    Bernd Silbermann

  4. , Department of Mathematics, College of William and Mary, Jones Hall 114, Williamsburg, 23187-8795, Virginia, USA

    Ilya M. Spitkovsky

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Dedicated to the 70th anniversary of Professor Vladimir Rabinovich.

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Rafeiro, H., Samko, N., Samko, S. (2013). Morrey-Campanato Spaces: an Overview. In: Karlovich, Y., Rodino, L., Silbermann, B., Spitkovsky, I. (eds) Operator Theory, Pseudo-Differential Equations, and Mathematical Physics. Operator Theory: Advances and Applications, vol 228. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0537-7_15

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