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Approximation in vanishing rearrangement-invariant Morrey spaces and applications

  • Kwok-Pun HoEmail author
Original Paper
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Abstract

Morrey type space built on rearrangement-invariant Banach function space where the set of smooth functions with compact support is a dense set of this space is introduced in this paper. By using the denseness of the set of smooth functions with compact support, we obtain the oscillation and variation inequalities of Riesz transforms on this Morrey type space.

Keywords

Approximation Morrey spaces Rearrangement-invariant Oscillation and variation inequalities Sublinear operator Extrapolation 

Mathematics Subject Classification

42B25 42B35 41A30 46E30 

Notes

Acknowledgements

The author would like to thank the referee for her/his valuable suggestions.

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Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Information TechnologyThe Education University of Hong KongTai PoChina

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