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Approximation in generalized Morrey spaces

  • Alexandre Almeida EMAIL logo and Stefan Samko

Abstract

In this paper we study the approximation of functions from generalized Morrey spaces by nice functions. We introduce a new subspace whose elements can be approximated by infinitely differentiable compactly supported functions. This provides, in particular, an explicit description of the closure of the set of such functions in generalized Morrey spaces.

MSC 2010: 46E30; 42B35; 42B20

Dedicated to Professor V. Kokilashvili on the occasion of his 80th birthday


Award Identifier / Grant number: UID/MAT/04106/2013

Funding statement: The first author was supported by the Portuguese Foundation for Science and Technology (FCT – Fundação para a Ciência e a Tecnologia), through CIDMA – Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013.

Acknowledgements

We would like to thank W. Sickel for calling our attention to the paper [36]. We also thank the referee for the constructive comments on the manuscript.

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Received: 2017-8-27
Revised: 2018-1-6
Accepted: 2018-1-8
Published Online: 2018-4-20
Published in Print: 2018-6-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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