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Removable Sets for Weighted Orlicz-Sobolev Spaces

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Abstract

In this paper, we provide a concrete criterion for sets lying in a hyperplane to be removable for weighted Orlicz–Sobolev spaces. We define porous sets and show that the porous sets lying in a hyperplane are removable; this is a generalization of the results in Karak (Potential Anal 43(4):675–694, 2015), Futamura and Mizuta (Hiroshima Math J 33:43–57, 2003).

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Acknowledgements

I wish to thank Professor Pekka Koskela, Dr. Changyu Guo and the reviewer for many helpful comments and suggestions. I would also like to thank the Indian Statistical Institute, Chennai Centre for financial support and for providing me a great research environment.

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  1. Indian Statistical Institute Chennai Centre, SETS campus, MGR Knowledge City, CIT Campus, Taramani, Chennai, 600 113, India

    Nijjwal Karak

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  1. Nijjwal Karak
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Correspondence to Nijjwal Karak.

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Communicated by Pekka Koskela.

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Karak, N. Removable Sets for Weighted Orlicz-Sobolev Spaces. Comput. Methods Funct. Theory 19, 473–486 (2019). https://doi.org/10.1007/s40315-019-00283-y

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